1) If miss your connection and you're booked on Delta, I don't see how you could suddenly decide to take the United flight instead, unless Delta somehow agreed due to the lack of other flights with them that night. Besides, you'd have to be sure that if you don't show up for the flight on Delta, the rest of your itinerary would still be valid (it wouldn't be if you were on the same airline as your arrival, but you'd switching).

2) Delta would normally put you on the next available flight, but that would apparently be the next day. Not sure they'd give you a hotel, since a late arrival at LAX wouldn't have been their flight. I gather you're already booked on Delta. Contact them if you want to be sure of your options.

3) When you arrive at LAX, you'll need to disembark, then go through Immigration (no way to say how long that'll take; depends on how many other flights land at the same tie, how many officers there are, etc.), then go through Customs (normally just handing over the customs form you got, and filled out, on your flight and which the Immigration officer will have initialed, though you could get pulled aside for inspection), and then, since you have no bags to hand over to a transfer desk, you exit the terminal, walk or take the free shuttle to your next flight's terminal, then go through security and to your gate. Two hours? Maybe, but I wouldn't bank on it. There are many LAX terminal maps onine, though you should always verify the terminal numbers since airline can change locations (e.g., Alaska Airlines just did).

4) Southwest doesn't have interline agreements with other major carriers, so you'd have to check in with them, and get a boarding pass, unless you were able to print it online (maybe hard to do as you're traveling) or can do that at one of their self-service kiosks.