There are several issues here:

• the verb should be in second position: "Jetzt starten die Fragen bezüglich mir" (still wrong)

• we don't normally use 'starten' in this context. 'Anfangen' or 'beginnen' would be more approriate here: "Jetzt fangen die Fragen bezüglich mir an' (still wrong / correct only in colloquial speech)

• 'bezüglich' is a genitive preposition. So, a first correct version would be 'Jetzt fangen die Fragen bezüglich meiner an' (correct but stilted)

• This sentence sounds very stilted. So, I'd prefer 'Jetzt fangen die Fragen über mich an'.

A correct way of expressing duo's original idea would be 'Jetzt kommen die Fragen über mich'.

Not really, but I use "starten" for cars, songs, games.