Cassette compatibility is not a concern, cassette sprockets don't care what's on the other end of the chain. BB30 crank will fit right into the BB30 bottom bracket. Front and rear derailleur capacity will be fine because you have less difference between chainrings (53-39=14, rather than 50-34=16).
You currently have a 10 speed drivetrain, and the Force 22 crank is for 11 speed. Chainring spacing is slightly narrower for 11 speed cranks as 11 speed chains are narrower than 10 speed chains. The opinion on this site seems to be that you can mix 11 speed cranks into 10 speed systems and vice versa.
As you say you will need a new chain because the length will need to be longer. You might consider a new cassette as well so you have a full new drivetrain. Front derailleur will need to be be moved up to accommodate larger rings, check this is possible on your bike. You should also check that your chainstays have enough clearance for the larger rings. A 53 tooth ring is about 6mm greater in radius than a 50, a 39 tooth about 10mm greater than a 34 (see this question).
My main concern would be compatibility with legs, as you will have a substantially (15%) higher spread of gear ratios. If you live in a flat area and never use your lowest gears you are probably OK, but if you are using your full gear range you may want to reconsider and stick with a 50/34 crank.