I have a 2x Shimano 600 FC-6400 crankset. Can I just replace the 3x RX-100 crankset with it? Will I need a new BB?
You can't directly swap them. They both use a square taper (JIS) bottom bracket but the axle length is different.
The 600 Ultegra FC-6400 uses an axle of 113mm for a 68mm shell and of 115mm for a 70mm shell. (Source: Shimano EV)
The RX100 FC-A550-T uses an axle of 122.5mm. (Source: VeloBase and Sheldon Brown)