I am upgrading my 1x9 drive train to 2x9 for some long distance tour and hills. Current set up is Shimano Sora 9 speed RD short cage, 9 speed chain, single chainring, Shimano Alivio 9 speed rear shifter. This is my BB:



I am looking at a sora 9 speed double compact crank set:
Shimano FC-3550 Sora 9-Speed Compact Chainset | Evans Cycles

Can my frame take this?
Also most I see most crank sets now are 10 speed, many people say 10 speed will work with the 9 speed system, but I also saw some people complaining shifting problems (I am not quite sure what they are talking about). So should I go with the sora one or try a 10 speed one?

Also I am really confused with the BB standards, so what kind of crank sets my frame can take? I only know mine is square taped. Thanks.