Is -taH a progressive/imperfective aspect, like English be ...-ing? Can I use it for the present tense and past tense as well as future?
Yes, to both. -taH is the continuous aspect: the action was ongoing before the time in question, and it'll still be going on after the time in question. Klingon also has an "in progress" aspect, -lI', which means the same thing as -taH except it implies the action has a known stopping point. -taH can be used whether or not there is a known stopping point. Neither aspect has any sense of tense built into it, so you can do the following:
wa'Hu' ram paqvetlh vIlaDtaH.
I was reading that book last night.*
DaH ram paqvetlh vIlaDtaH.
I am reading that book now.
wa'leS ram paqvetlh vIlaDtaH. I will be reading that book tomorrow.
It doesn't always equal English -ing, but the two are very similar. Because we rarely use the simple present tense in English and prefer to use the present progressive, DaH paq vIlaD and DaH paq vIlaDtaH might both be translated colloquially into English as I am reading the book. But the two Klingon sentences say somewhat different things.
My answer of "I can read that book ..." was not accepted. Is this an omission or a subtle point that I am not picking up on?
"Ram" specifically "night"? "Evening" not accepted. What would be the translation for "evening"?
At least one dictionary definition says it refers to both the latter part of the day and the early part of the night.
As for "good evening," it's just a formula, and doesn't say what it literally means. You can also say "good morning" and "good afternoon" for both greeting and departing.
And what is the difference to "I will read that book tomorrow night", which seems also to be wrong?
The -taH verb suffix indicates that it will be, not just an activity which will occur, but an activity that will be ongoing or that during which something else will happen. That's why it is appropriate to translate it into English as "I will be reading that book".
The English tenses and the Klingon aspects don't really line up. Depending on the context, there can always be ways that one aspect might line up with any particular tense. For instance, if by, "I will read that book tomorrow night," you mean that you intend to spend the whole night reading the book, then it might be an appropriate translation of the given Klingon sentence. However, to keep clear the difference between stating that you are going to spend at least one moment reading the book versus going to be spending ongoing time reading the book, in this course we ask that you translate the ongoing aspects (-taH or -lI') with the English progressive tenses (i.e. using -ing) even thought it's not a perfect correlation.