> I don't have any TAs, professors, peers etc to ask or grade my stuff when working my way through a text book in my spare time. How can I be sure I understood stuff correctly?

I definitely agree with you on this. However, there are three things self-learners (or even students) can do.

1. Find a textbook with worked solutions or a different presentation of material.

2. Look for course material that has problem sets with solutions, worked tutorials, or worked examples.

3. Learn numerical or other methods to evaluate your solutions. I know this isn’t possible for proofs, but if it’s an algorithm’s run time, I don’t see how implementing the algorithm and plotting run times over different input sizes wouldn’t be a good way to see if you have the correct run time.