None of the doors are undercut. And no room has an individual return vent. They all come about as close to the floor as possible without scraping. About how much should they be undercut?

With no returns, you likely have a terribly inefficient total HVAC system that needs much more than door undercuts in order to function adequately. Get a consult from a local HVAC specialist to address the air flow issues, and to address balancing the system pressures in the home. You’ve passed the point of guessing on the Internet.

Of course you could leave the doors open (most of the time).

I have no idea about the weather stripping issue but the interior doors need to have a space between the door and the flooring and and no returns you get a very inefficient HVAC system so talk to a pro about fixing the issues you have .My guess is the tile was not the original flooring.

Undercutting doors is probably not going to make your HVAC system more efficient and save energy costs. It will help even out the temperatures of rooms with closed doors. There is potentially some savings if you can readjust your thermostat setting after you improve the air return flow.

Before you start cutting doors and hiring professionals, I suggest you try a simple test. Turn the fan on in the bathroom and hold a piece of tissue paper by the bottom the door. How much the the tissue moves will indicate how much air is being pulled by the fan. You can repeat this test with the HVAC on in all your rooms.

If the tissue is not moving then that means air is being pulled from somewhere else and cutting the door is not going to add much in air return. If the tissue is moving and you feel air flow, then undercutting that door will help for that room. In some cases the return air pull is so strong it will force a partially open door closed if it is set to swing towards the return.

If you're seriously going to trim the door the gap size will depend on the supply duct size to the room. You'll need the cross sectional area of the duct in square inches and make the door gap as large as the duct area or bigger.

A round 5" duct has an area of 19.64 sq. in., a 6" duct's area is 28.27 sq. in., a 7" duct is 38.47 sq. inches. If you have rectangular supply ducts multiply length by height for the sq. inches.

Then cut the door gap to equal or exceed the sq. inches of the duct. So a 28" wide door would need to be trimmed 3/4" for a total gap of 21 sq. inches if the room has a 5" round supply duct.

I'm sure you can do the math to figure out the different door and ducts sizes. It isn't the proper solution but will help to alleviate individual room positive air pressure and as far as the bathroom exhaust fan you want to alleviate negative air pressure. if you have a 50 Cubic feet per minute exhaust fan installed in the bathroom a a 3/4" to 1" gap will work fine. If the fan is 100 Cfm the gap should be 1 1/2" to avoid negative air room pressure with the door closed. If you have a 200 CFM exhaust fan in the room you may as well remove the door.

Providing a greater gap under the doors will help.

Remember when it comes to exhaust fans, no air gets exhausted without outside air available to replace it. Whether an exhaust fan in a bathroom or one in the kitchen over the range, there needs to be some makeup air available. Older houses are leaky and sometimes that's enough but relying on that pulls in less than fresh air from dirty places - the attic, through the walls, from under the house.

Newer houses, and especially those in places with extreme temperatures, are sometimes required by code to have some form of makeup air system built in. Otherwise, the simplest and cost-free solution is to crack open a window. It doesn't need to be in the same room, in an adjacent room is fine. In addition to providing fresh air which most houses need anyway, it will make the exhaust fans work much, much better. Try it, you'll see. Even on a still day, if you crack the window and turn on an exhaust fan, you should be able to sense the incoming air flow on your hand.

I forgot to mention - another alternative for bedrooms is to put in jump ducts.

from what I heard, yes, you need to have a gap under your door, or leave your doors open a few inches. we leave our bathroom door wide open when showering, our fan doesn't do a good enough job on it's own.

if you don't want to do any of those things, one creative workaround would be transoms:

of course an undercut is an easier solution, and better than doing nothing. in my home, I need the gaps because there are rugs nearby. also they allow a little bit of light in at night.