Should a Brahmachari wear Angavastram? If yes, during which occasions? Can a Brhamachari perform Perumal Tiruvaradhanam if the elders of the home are on a travel?

There is no need for a Brahmachari to wear Angavastram.
If the Brhamachari has undergone Samashrayanam, has undergone Ahnika Kalakshepam, and has been preached Tiruvaradhanam, then he can perform so.