It's possible to buy tickets from the box office (not the turnstiles) on the day assuming the match isn't sold out. I'd definitely try to pre-book tickets.
Usually Fulham are a good bet for tourists as they don't often sell out but the Chelsea match is a local derby against "glamorous" opposition so you may be out of luck. The best sites for buying tickets are the websites of the teams involved.
Reselling football tickets (touting) is illegal, in fact football tickets are the only type the law prohibits the street re-selling of. That being said, it is very common - a walk around the street adjacent to the ground will show you many transactions. It's worth noting that buying touted tickets is a crime (not just selling,) obviously you have no legal comeback if your touted ticket doesn't work and even though you might see some police turning a blind eye there's no guarantee they all will.