Crossing US border just to take another flight and times/rules to be considered

I am planning a trip to Bangkok, Thailand (BKK) departing from Lima, Peru (LIM) and I'm a Peruvian citizen.

I am making my own itinerary since I found cheaper prices when booking flights separately.

Here's what I am planning to book:

But the following questions came up:

1. Is there a problem to cross the US border through LAX just to take another flight? (Holding a B1/B2 visa and 2 times, one on my way to BKK and another when going back to LIM)

I mean, I know immigration normally stamps your passport with the maximum time that you are allowed to stay but, since I will enter the country and then leave in some hours, I don't know if this will be a problem or not (when re-entering the country) or if I'm ignoring something like a rule that maybe I should know.

2. If there's no problem with the 1st question then I'd like to know if the times between each flight that I am planning to book are fair enough.

So, I know the times to go through immigration/taking your bags/customs vary from airport to airport but maybe someone knows better about LAX. Apart from that, on each flight I am considering the 3h needed before each international departure and some extra time in case of a possible delay. However, I am especially doubting if the time before taking the flight from LAX to LIM is enough.