Answer to your first question:
It's possible but without intervention from a beekeeper, it's doubtful. A swarm usually relocates AWAY from the "parent" colony (has to do with pollen & nectar foraging distances). Rarely, it can happen in a natural way but as I said, it's not likely. There are certain manipulations a beekeeper can do to "entice" (or more-or-less "force") a local swarm to stay put. There are at least two or three techniques that can be used; most all of them begin by physically capturing the swarm in a hive box, then doing such things as giving them an open frame of brood (to "lock" them in place) and/or immediately requeening and/or performing another split (depending on the size of the swarm) and/or feeding them sugar syrup, etc. A new swarm will look for a certain sized cavity in which to build their new combs - which they will build very quickly once they're settled. They also like the smell of old comb - it will attract them - as will a queen pheromone lure. You have to do a lot of reading and learning; beekeeping is not just a question of putting bees in a box and then forgetting about them (contrary to what your wild chimney hive would have you believe).
Second question:
A well established colony can throw off multiple swarms each year (one - two - four - eight) - each progressively smaller and usually in the Spring (but also, sometimes in the Fall, typically).
Third question:
There's no "set" distance. Once the swarm has decided to stay and has begun to defend it's home, it can be very close to another colony. My hives are typically four or five feet apart so I can work them easily. Some migratory beekeepers have four per wooden pallet, with entrances facing different direction.

Thank you txbeeguy. After reading some of the previous posts, it would seem wild bees are pretty much on the way to extinction. Very sad. I had hoped it would be as easy as providing them a hive and they would live there happily ever-after.

I did not realize that wild bees were a danger to beekeepers because of parasite spread. When the hive swarmed last year, I could not find any beekeeper to come for the swarm. They remained on a tree limb for over 2 days, then disappeared. Is it safe to say that allowing them to remain wild is a bad thing for local beekeepers? If they are doomed to eventually die from mites, their empty hive will remain to infect any other bees in the area? This is all very depressing.

As I have posted previously at other websites: we will ALWAYS have wild honeybees. When you read about the supposed extinction of wild bees, it's mainly hype. That's not to say there may not be bad times ahead but I believe the genetics to guarantee the survival of Apis have already been released into north America (primarily via the USDA Russian queen breeding program). In the originating location of the parasitic mite, Varroa, in the far eastern region of Russia (Primorsky Cry), honeybees have co-existed with the presence of Varroa for about 100 years. So the total and permanent decimation of wild honeybee colonies in America isn't very likely.

A very similar thing happened in the British Isles just after the turn of the 20th century, with the invasion of the parasitic tracheal mite. Virtually all colonies having the old English 'black bees' were killed off - however, a few survived, from which a Benedictine monk, named Brother Adam, culled the survivors and eventually developed today's very popular breed of honeybee known as the Buckfast bee. So don't be depressed, sometimes good things do come out of bad circumstances!

Wild bees are not a huge risk to beekeepers because (1) wild bees are so low in number now as to be nearly inconsequential. And (2) the bees in your case swarmed generally meaning they were healthy and multiplying and hardly heavily infected with the virus vectored by varroa parasites.

You can usually easily catch a swarm if it's low enough to reach without endangering yourself. They're hardly likely to go into an empty hive you have nearby -- although it has happened -- although they'll possibly stay put in one if you put them in one with at least one frame of drawn comb and the rest filled with foundation.

Wild bees (more correctly, FERAL bees) may be a solution to our mite problems. Presuming there are a few tough resistent colonies out there... if you find one, get it in a hive, it might be our long sought super bee.

I am sure this does not happen often but!!! I am a first year bee keeper and have not even received my order of bees. I set out my hive in preparation for my order of bees that should arrive fairly soon. My hive has been outside for three days and I noticed bees flying around it. I checked it out and found it full of bees! Now I am in a rush to get another hive set up before my ordered bees come. Just about every year in my back yard I get swarms of bees. I do have city power lines that run behind my house which I believe may have something to do with this, not sure though. Oh well I am very happy to have the bees!!!

snlecher, I had the same thing happen to me. I assembled a top bar hive last march and put it out on sawhorses in the middle of our acreage under the shade of a gum tree. In June, I remembered about the hive and went to make sure it wasn't knocked over or destroyed before I went through the expense of ordering bees for it.
I found it to be just fine, and occupied with a very vigorous colony of feral bees! I was so happy! I did nothing but assemble the hive and set it out there. No lure pheromones, no old comb, nothing. I just left it alone and they came. Since then, I have only moved the false back up to help them through winter, then moved it back again this spring to give them more room. I did not feed, or fumigate, or really check on them at all. I went this weekend, and it appears that they are preparing to swarm, so they must be doing well. I will let them do as they wish, as I am only providing them a home so my garden will have pollinators, and to help the local bee population. They are very docile. My hubby was able to open the hive and move the false back with no protective equipment and no smoke and he did not get stung. We mow a path right by the hive and they do not attack the mower.
Its a myth that the feral bees are dying. I put a bit of honey on my back porch table, and the bees that came to take it flew off in three different directions. I am the only beekeeper for miles around here, so I know there has to be at least two other feral colonies nearby somewhere.
I think the commercial bees are the problem, not the feral ones. The commercial bees are the ones that are weak and need tending. The wild ones seem strong and healthy and don't need any help.

Feral bees are European Honeybees that have flown away from managed hives..

Feral bees can carry exotic bee diseases and mites (Acarine mites, Varroa and European Foul Brood disease), therefore controlling bees can remove this threat to the Managed honeybee industry & concern to apiarists & hobby bee keepers in Melville.

Feral bees out compete native birds and animals

The threat of feral bees out-competing native bees (there are over 2000 species of native bees which are at risk of extinction).

Here is a link that might be useful: Frequently Asked Questions

I have a local cafe in a rural part of ohio that we visit. They have a tree with a golf ball sized hole that my son noticed tons and tons of bees flying in and out of! Amazing to watch we suddenly realized that above our heads without us knowing were 100s on bees, just being bees! I spoke with the owners and they have planned to kill the bees as they have a play set and lots of patrons. They tryed to kill them last year but to no success they are back.... I spoke with local bee keeper he can not do anything with them in tree, but the thought of the bees being killed.... not ideal. Any thoughts on a way around killing them, or chopping down the tree. My dad kept bees and I have always wanted to do the same.... is it possible to get a hive of my own off these bees?
I can not figure out how to post a new thread.... feel dumb but I spend more time in garden then on this machine lol.

Getting a colony out of a tree can get very tricky and cumbersome if you don't want the tree to cut down.

Cutting down and open carefully would be the easiest but no guarantee that you'll get the queen out alive.

This is how I would approach it,...screw some angle brackets onto the tree and set a hive box up with foundation [on top level of hive in the tree] or if you have a frame or two of new brood from another hive, bees want to tend the brood so you'll have some of the local bees going into the box right away and stay,...how?
Seal off all entrance from the tree, except one, the highest on the hollow, there you attach a hose/tube, perhaps staple fist a screen, shaped into a funnel, onto the tree, funnel into the hose going into the bottom board of new hive box, [drill hole first, perhaps using something like a one inch rubber tube.

All bees will have to go through the hive entrance, going and coming, hopefully the queen will go up when the tree hive gets filled up, bees and queen love to go up, never funnel downward. Check one's in a while, about one's a week and see it you have new eggs/brood, this will tell you that you have the queen, then undo the hose, perhaps move the box a bit, and smoke out all bees out of the tree and shut close.

You'll have some angry bees /swarm around and looking for the home, eventually they settle down and go into the hive box.

Brood in the old hive will die out,...open up about Sept. and let bees rob out the honey in the tree, this can take a couple of weeks, when no activity, seal up again, otherwise a new colony will move in again next year.

You can open briefly in spring again to clean out some more if needed.

Timing is important, do it in early summer when the colony is expanding, don't do it in fall.

I know, easier said then done.

Perhaps I will start a new thread