The width difference of 10 and 11 speed chains is very close (5.88 vs 5.62mm) so usually this works without issue. There is always some possibility that even this difference will cause rub against the large ring in some of the small/small combos. Very short chainstayed bikes like yours increase the likelihood. Chainring micro spacers such as the 0.2mm FSA are the fix if there are issues. You'll also need to make sure your FD can be moved up a little, but that shouldn't be a problem.
You haven't said what kind of BB shell your frame has. If it's threaded you need any ISO/BSA threaded Shimano road bottom bracket. If you've got FSA cranks with a 24mm spindle now then you can use your existing BB if it's not worn out. If it's BB30 you have the option of using any of the myriad adapter systems for 24mm cranks, which consist of reducer bushings, press-in shell adapters, and screw-together adapter bottom brackets. There are many questions here about the pros and cons of these systems. Your bike's cable routing arrangement in some cases can inform which is best.