Yes. That's what pigtails are for. No problem at all.
Incoming (from panel) wires -> LINE side of GFCI
Outgoing wires - short pigtails (colors matching the outgoing wires, normally black & white) -> LOAD side of GFCI
On the other end of each pigtail, wire nut the two matching wires to the other locations.
All grounds (both sides) are connected ...
Yes, as long as you're connecting the wires at the load end, the GFCI doesn't care how it's connected.
You'll have to install a large enough box to accommodate 9 wires coming into it though.
According to this chart https://www.bhg.com/home-improvement/electrical/how-many-wires-in-an-electrical-box/ You're not going to be able to use a standard 3 x 2 box (...