If you choose to. Nobody is forcing you into fights or tournaments. Amateur bouts are run by different sanctioning organizations where they hold matches and tournaments all around the country and even outside of it. Its not uncommon to match up with Canadian, British, or Irish teams.
Yes. I knew some father - son teams where the dad would fly himself and his son out to different tournaments around the US, got his kid maximum experience. If you live in southern california you don't have to travel far though, tons of tournaments and events all over.
Depends on the level you're fighting at. If you want to compete in WCs, Olympics and other big international tournaments, of course you have to travel because the US is not the center of the world which holds all big amateur boxing events. Obviously you can stay inside the US if you "only" want to compete in the Nationals or something else like state GG.
You pay for it yourself. There are many good boxers that win local and regional tournaments but can't afford to travel to the tournaments they qualify for. Many gyms try to get sponsorship from local businesses or have regular fundraisers.
Outside of SoCal a kid is going to have to travel if he's any good. even in big cities like Chicago these days there is not a plentiful amount of amateur boxers - let alone stand out amateurs in every given weight class. If a kid is serious about placing in the national tournament he's going to have to travel the country for the requisite experience. Travel is all outta pocket. Gyms do their best to fund raise for kids.
International boxers that are in a program(high performance national team etc.) have no fee's to pay. All expenses paid excluding money for snacks etc.
