Bathroom Electrical question GFI
Yes, you can do exactly what you propose.  Just make sure the box you use is large enough for the splices. 

You'll need at least a 4x4x1-1/2" box, which would be literally at full capacity. A 4x4x2-1/8" box would be a much better choice.

No, you do not need any GFI devices downstream of the first one, provided you wire the line in to the LINE terminals, and the line out to the other receptacles to the LOAD terminals.