If I am a SQ *G member and looking to book a wholly domestic (LAX-EWR) flight on UA Basic Economy; would I be entitled to a free checked bag? I have tried calling the UA 800 number but have received conflicting / confused responses - so I thought this would be a better place to ask.

Further complication and second question: Although I am a SQ *G member (and have my SQ card to prove it), I would like to credit this flight to another *A program where I currently have no status. Do you see any problem is this scenario? Thanks!