what are the cheapest seats in theater?

If money is the issue and you really like theater, you might be able to volunteer as an usher. There are several perks (like time with the actors) that go along with seeing the show for free.

It varies from theater to theater, but generally the farther back the seat is and the higher it is in the bacony, the cheaper the seat (so if you're in the last row of the top balcony, your ticket will be the cheapest). Sometimes limited view seats go for incredibly cheap, these tend to be the seats on the side and in the boxes since you can only see part of the stage rather than the whole thing. If you're at a Broadway or West End show you can also get really cheap seats the day of for about $20 or $30 and these will usually be front row or close to it.

As others have said, it varies. As a starving actor myself, I do student rush, which is generally the cheapest you can get, but only if you have student ID. I've also found some theaters have standing room. The cheapest ticket I ever got was 10 pence, standing room at The Royal Court for Clyborne Park, which is now reopening on the west end. The most I've paid is 27.50 (pounds, not dollars) and that was for Into The Woods in Regent's Park.

Broadway is significantly more expensive, even for students. Expect to pay around 40 USD for a student ticket to a big show.

It'll vary, but which ever is the worst seat, will be the cheapest.

Typically these will be in the back of the balcony.

If cheap is more important than viability, get yourself an "obstructed view" seat. Some theatre's balconies will have "leaner" seats in the front row where you could only see the stage if you lean forward the whole time. I recommend these. They are usually cheaper and pretty good (just not super comfortable)

It varies from theatre to theatre, and sometimes from show to show - it depends on the configuration of the set as well as that of the actual building.

Last row upper balcony.

the farthest ones away from the stage.