If you paid for a lap infant, almost certainly paid a 10% fare. There are exceptions, like for Canada which you only pay certain taxes but not the fare, but even then, I think they generally get the same allowance as the adult, which for Canada is 0 anyway, plus any premier status additions. Obviously, no charge for domestic lap infant.

generally, if one person on the same PNR has status, those benefits apply to all, so that is a yes for premier benefits. The exception is if the allowance is inherited via credit card benefit, which is limited to 1 additional pax, which could presumably be another adult or a lap infant. Also beware of any direction where you must check in with a partner carrier - in that case, you will not get the benefit of any bag fee waiver that UA gives you - if it’s a *A carrier and you are *G, you’ll get whatever that carrier gives to a *G traveler (usually not the same as UA gives - most don’t have the higher 70lb allowance, for example), but if it’s not a *A member (like, for example, Viastra in India, CX, Hawaiian, Jetstar, etc.), you’ll just get the normal allowance and not based on any status (or UA card) benefit.