I don’t know how long I haven’tit's been since I've watched TV.

It's more common to see the phrase "how long it's been since..."

I don’t watch the affairs of the state because I am just an ordinary person.

I'm not sure what you mean by "affairs of the state" ... do you mean the news? Do you mean government broadcasts?

I don’t watch the TV play because I think I can write it.

Not really sure what you mean by this, so I can't correct it. A "play" is a theatrical performance, so you would go in-person and watch actors perform. A "show" or "program" is what is on TV.

I don’t watch historical playshows because they are all past and they arefrom the past and not necessarily real.

Read what I said above about plays vs. shows/programs.

You already wrote "they are", no need to write it twice in this scenario :)

Is there anything else I can seewatch?

saying "watch" is better than "see" because you "watch TV"

I (should) take advantage of the time ofI would waste by watching TV to study, and I think this is a smart choice.

I put parenthesis around should because it sounds like you already do this. If you do, the should is not necessary.