Ants don't cause aphid infestations. And grits won't get rid of ants, sorry. Under normal conditions, ants should simply be considered a natural part of the outdoor environment. When their (ants) populations become very excessive, you can purchase a granular ant bait product containing Spinosad. It's proved to be very effective in controlling a wide variety of ants.

Neem, when used properly, is very helpful in controlling black spot and aphids on roses. Read and follow the directions carefully, as you should with anything that you apply to your plants.

Keep the clover mites washed away with plain water or a soapy water spray.

We really can't help with all of the other things without an accurate identification.

I am very reluctant to prescribe pesticides, but in an urban situatuion like yours, with a seriously out of balance yard, you may need to use some at first to get the situation under control. While I have heard good things about neem I have not seen it very commonly in garden centers. You may have good luck finding it. If not, I would suggest using Merit, which is put out by Bayer. Read the directions, use judiciously, and only long enough to get the aphid situation under control. If you try the organic methods and they work, then disregard this suggestion. You are absolutely correct that indiscriminate use of pesticides will just throw the balance of the yard off further. That's why I particuarly like systemic pesticides for sucking insects as they don't kill the predators like some sprays and powders do. Oh, BTW, I had good luck with pyrethreum dust for my roses. It's a chemical, and toxic to fish, but it does break down. That's the negative of it, it needs to be reapplied after rain. This is not as good as a systemic, IMHO, because it is indescriminate, will kill butterflies and bees. The only good thing about it is it will eventually break down. You can use it to get a serious problem under control and then hope that the balance re-establishes itself after the insecticide breaks down.

In the long run, I would suggest changing mulches to something less acid. Roses don't like acid soil. Also look into some compantion plantings for the roses. Last but not least, my system for roses is if I have a plant that is continually getting infested that means it is just not the right plant for that spot. There are so many hardy roses options, I suggest slowly replacing the worst offenders.

Sorry systemic insecticides can kill any insect that uses the pollen or sipes the necter. Since bees and butterflies do both it can kill them if the concentration is high enough. A big plant may not present a problem but on a small plant you might be getting rid of the insects you are trying to attract.

As Rhizo stated the ants are not the reason your plants have Aphids and if your plants are infested with many insect pests using broad spectrum poisons is not the solution since they will only compound the problem by continuing to kill the beneficial insect that could help control the insect pests. Neem Oil, pyrethin based products, the Bayer Systemic, Sevin (Carbaryl), and most others are all very broad spectrum poisons that kill insects indesciminately.
If your plants have Aphids an easy control is as simple as a sharp spray of water, but plants infested with pests are not growing in good, healthy soil so you need to look at your soil to determine why the plants have these pests. What is the soils pH?
How well does the soil drain?
How well does the soil retain moisture?
What kind of life do you see in the soil? Earthworms, centipededs, millipedes, pill bugs, etc.
How much organic matter is in that soil?
How is the nutrient balance?

I'm so glad you brought up the soil topic K. I was thinking about it and was going to post back today about this anyway. In any garden, but particularly a neglected urban one, most problems begin and end with the soil. I would have the soil tested, and do some research on the plants you have growing together in the garden. Do they like the same kind of soil conditions? That is crucial. Because otherwise, if you ammend the soil to make one kind of plant happy you might make its neighbor unhappy. And there's a lot more to soil than just pH and nutrients--soil structure, microbial action, and drainage are just a few major aspects.

A garden is a system and pests on one plant might be a symptom of problems with the whole system, not just that individual plant. Adding compost NEVER hurts, so start a compost pile and/or find a good compost source. If I'm not mistaken, I think roses like composted manure, but I could be wrong.

I'm also a firm believer in companion plants. Not because I think they have some kind of mystical relationship, but mixing and matching your plants makes the juicy ones harder for the pests to find. Off the top of my head, good companions for roses are tansy, rue, chives and maybe even those pyrethrum daisies. Maybe mums too. And yarrow is a good overall companion.

Also, most roses don't like shade, and I would imagine a bamboo planted close to a rose is sucking all the nutrients away for itself. You might consider installing some kind of flashing around the roots to keep the bamboo roots confined--although that is going to be tough in the long run! I'm not a bamboo fan due to the work it takes to keep its agressive nature under control, but I know a lot of people love it for its form and privacy it provides.

The organic methods, when used consistently may get your problem under control. I am loathe to use these higher level pesticides in my garden because as I said, it throws stuff off balance. But if your garden is out of balance anyway, you may have to either use them or loose some plants. I have only used a systemic once, on a grey birch tree that was infested with scale. I was using a less toxic oil spray on them but it was not working. The tree was dying and the systemic helped save it. I know I paid a price in my soil. I couldn't find anything on how long the systemic would persist in the soil. Pyrethrum does break down relatively quickly--I can't remember exactly, either 2 weeks or 2 months, something like that, different formulations have different active periods. It is a broad spectrum insecticide and will kill the beneficials. But unless you live in an area with some type of endangered butterfly or something, insects are very prolific and a natural population will reinhabit your yard, to be sure. The pests will too, so all the pyrethrum is doing is buying you some time until you can get your roses healthy again. I still wouldn't advise it unless it was a matter of life and death for a plant. But I would also realize that nature will replenish an insect population unless you have destroyed the habitat. There are also things you can do to attract beneficial insects into your yard, which you can find out a lot about by researching.

Take a looks at your yard as a system and see what is working in your favor and what is not. Begin to reorganize the garden so it is more in harmony with its environment. I have come to realize that it's "survival of the fittest" in my yard, and if a plant succumbs, that's the way it goes, time to plant something more suitable. Eventually that way you get a yard full of plants that can survive on their own, with minimal fussing from you. So I'd attack the problem from many angles, starting with the soil, the types of plants and the growing conditions.

But occasionally, if it's something I really love, and it is a matter of life and death, I will use a stronger pesticide. But with full knowledge of the tradeoffs. Below is an interesting Web site I found when searching for the breakdown time of pyrethrum. Looks like notes from a college course.

Here is a link that might be useful: Insecticides