Jodi, I had a similar concern my first time flying into Heathrow, I'd heard horror stories, and how big and confusing it was. So I think I budgeted an hour or more for getting my luggage and wandering around lost and confused and trying to find my way.
I had all the same basic needs at you (except #4, don't quite get that one), find an ATM, find the tube stop, head into London.
Anyway, after planning that it might take me two hours to get situated, I think within 15-20 minutes of getting off my plane (I only had carry-on so no waiting for luggage), I was sitting on the tube on my way into London thinking, "that was way easy!"
Also the tube web-site has all the information you need (Google: London Tube), so you won't even need a map right away, and it looks like Earl's Court is right on the Picadilly line from Heathrow
If you can see and read and have ever navigated any major US airport you won't have a problem!
Don't be nervous.