Is it possible to change
without changing the meaning?
No, these two sentences are different, and you have to use the first sentence in 99% of cases.
The first one is easy:
Is this necklace what you bought? / Did you (really) buy this necklace?
The second one is difficult:
Is this necklace what you would buy (instead of just looking or borrowing)?
Are you thinking of (actually) buying this necklace?
This is an euphemistic version of このネックレスは買うんですか. Sometimes the past tense is used to express euphemism, just like in English. This sentence is not very polite and sounds like a broken マニュアル敬語 to me, but a native speaker may say this at a shop to someone who is a bit higher than him.
No. If you want it to be past, you will change the other verb into past and leave んです/んだ as it is. Only your first one is grammatical.
However, it is technically possible to have んだった, but only in the -ら conditional form: んだったら. You wouldn't see it at the end of a sentence.