Is it okay to post textbook solutions online?
While I don't think there is anything formally standing in your way of doing this, as long as you don't post the questions themselves or answers from the publisher's answer key, I don't think that it is a wise thing to do. 

But I'll focus on future students rather than professors to explain why it isn't wise. For many things the only real way to learn them is to practice. This is true in math and the sciences as well as in, say swimming or chess. Learning involves changing the brain. See, for example, the book The Art of Changing the Brain by James E Zull.

The implication of this is that, very often, the most important part of a published textbook is the exercises, not the explanatory text. Students need to, perhaps, struggle with those exercises to learn the material. If you give them a shortcut to getting the answer, while it feels good to them, it makes it harder for them to learn the material. Too many students don't understand this (hence the need for a book like Zull's). It isn't a question of being able to turn in "homework" as much as it is having useful practice exercises that you can't short-circuit. 

If you want to meet your own goals and also publish something useful, publish a set of additional exercises for a good book instead of answers for the existing exercises. You will find (a) that this is harder and (b) that it increases your own knowledge by changing your own brain. 

You could also, as some publishers do, publish solutions to half of your questions. Some textbooks, for example, have solutions to, say, the odd numbered exercises in the backmater. 

You might even get an offer from a publisher to do that for other books. Some textbooks, in fact, have the questions provided by other than the author. 

But publishing answers is a disservice to other students, not a service.