Do determinacy of one-step evaluation and uniqueness of normal forms apply to all (or most) languages in TAPL?
Uniqueness of normal forms definitely applies. This is still a theorem you have to prove, but if it doesn't hold, what you have isn't really a normal form. The whole point of normal forms is that there's a unique form for each value, that's what makes it "normal".
For determinancy, I think it holds for most languages in the book. Usually when you're defining a small step semantics, you try to do it in such a way that it's deterministic. However, there are notable exceptions to this. First, if you have a general rewrite system, like the untyped lambda calculus, then it's totally valid to have non deterministic reductions. This is what lets us talk about Church Rosser and the diamond property. Secondly, if you have a language with any sort of concurrency, then you probably want to have non deterministic rules, to model the different possible orders of evaluation, so that you can show your language is well behaved regardless of which interleaving is taken.


That said, I want to be clear that these things do not come for free. They hold for the Languages in the book because Pierce has been very careful to ensure they hold. It is easy to accidentally definite a language where these do not hold.