score:9
You won't need a visa; US citizens are allowed visa-free entry to Britain.
Go through arrivals
You'll need to pass through security to get airside again.
It can take an hour or more each way to get through passport control and customs, and security. Check with BA how long they recommend, but expect to need 1-2 hours to clear on arrival and the same when you return for your connecting flight.
If you're booked through with one airline on a single PNR, I'd expect your luggage will be interlined, and you can just leave it. Check with BA.
Not sure what you mean here. You'll need Sterling, but you can probably get away without if you have Visa or MasterCard available. Amex is less widely accepted.
If you're hoping to meet your friend at the airport, this should all be fine. If you want to go into central London, this will be tight, and if your inbound flight is delayed, maybe not even possible.