1. "...is payment for Airbnb places always processed in the US even for stays overseas?"
Airbnb processes reservations for guests in their own currency, pays out in the currency of the host. So you, in the US, will always pay in US dollars, a UK resident will pay in £s, etc. The host posts prices in their home currency and when a guest in another country logs in and searches/books, the price is converted by the website at the current exchange rate and they always see the rate in their own currency. So, presumably, the transaction must be processed, the charge from the guest, payment to the host, each in each country.
I find one of the very attractive things about the site, when reserving outside my own country, is the fact that I see and pay the rate in US dollars, always know exactly what it will cost and pay no conversion fee. And it's similarly straightforward for the host dealing with overseas visitors.
2. "...how much pre- trip communication with hosts is the norm?"
As a host, I find the amount of communication varies widely, there really is no norm. I respond to each communication and some guests, or even those who are just inquiring, message a number of times. Some I don't hear from at all except for the reservation request and maybe a "thank you", or estimate of arrival time.