I would personally say either is fine, but since this sentence would be said as a comment to someone being able to read you, can is generally not used. Although if talking about someone else, "he reads me like a book" sounds more natural than "he can read," but both are okay, I think.
I would still add it as an option.
It's very frustrating when you do understand the Ukrainian sentence, and when your English translation is not the best because you're not a native speaker of English, or a native speaker of a different dialect of English. That's not an English course, after all, that's a Ukrainian course.
The course seems raw because so many options are omitted, you're doing god's work adding them, and I believe it's better be safe and add all possible variants, if they are not clearly wrong, of course.
OK, thanks for your comment! I would add it because "ви бачите мене наскрізь" not as a comment to some particular event, but rather as a statement in general gives a feeling of "you can read be like a book" at least to me. And yes, I think the main thing is to make sure the learner understood the Ukrainian sentence, so all kinds of variations, slang and regional versions should be included in the English translation (but not necessarily into the Ukrainian not to confuse people).
I'm not always sure my opinion coincides with the rest of the Team, but let's see :D