5') The music Tom is playing is Beethoven.
That's fine, in a sort of colloquial sense (think of it as omitting "by" between "is" and "Beethoven"), but there's a problem with the use of "a" in the original. Using an article suggests that it's modifying a regular noun, but Beethoven is a proper noun. It's a bizarre combination. It also can't be suggesting any such shortening unlike the revised version above.
If so, can you also say these?
5a) Is that music the Beatles?
5b) This play is Shakespeare.
Again, fine, but you're actually dropping either "from" or "by" between "music" and "the" in 5a, or between "is" and "Shakespeare" in 5b. I wouldn't recommend actually using this technique as a second-language English learner in general; English is not very permissive when it comes to truncated expressions like these, and they're never necessary or even particularly expected.
Can't you say (7)?
(7) Is that the dictionary you've bought recently?
You can, it's just a little jarring. That form is usually used in a context like this when you have reason to believe it's happened multiple times, which is of course highly improbable with the action of buying a dictionary. Not wrong, just an odd choice.
How about this?
7f) I've bought this dictionary recently.
Again, not wrong, but you'd be more likely to hear "I bought" rather than "I've bought" in this context.
About 10, how about this? Does it sound off, too?
(10a) Paris is a city I visited last year.
Honestly, I don't agree that it has to be "was", because in 10, "is" is connecting "Paris" to "city". (Note: Paris is not a town, it's a city. Towns are smaller settlements; it's a bit arbitrary where you draw the line, but the well-known cities around the world, the big ones, are never referred to as "towns".) And yes, 10a is fine.