Haven’t tried regular-sized choc switches before, but they should work. One thing to consider would be that with the heigher switches, the scroll wheel might be harder to reach with the thumb because it might be physically hidden behind enter/space. Should not be a problem it you are used to use the index for them though.
No, you solder it in the same way for both sides.
The “flipping” is handled mostly internally. For The right hand side, the firmware just maps the rows and columns differently than for the left hand side. For pins where this is not possible (Vcc, Gnd,…), there are jumpers on the other side that need to be soldered.