I don't believe it is correct to use both backstabs and screws. If it's legal, it's not a good idea, partly because backstabs are notoriously unreliable.
Also the socket in question is a 50 cent builder grade special, all the more reason not to use backstabs or the socket itself. A much better choice would be a $3 screw-and-clamp type such as Leviton, which allow 2 wire connections per screw, easily handling those 3 wires each side.
It's fine to use any box as a junction box. I do it all the time, a switch or outlet box is a good place to do it since they have to be accessible. Just watch your cubic inches. For instance, in that box I see
- 1 count for all the grounds combined
- 8 counts for the 8 conductors present
- 2 counts for the yoke (not caring if it's a thin little switch or GFCI)
Total 11. Given their fondness for backstabs (well in fairness they are using screws wherever possible), this had better be 14 AWG wire. (Backstabs won't fit 12AWG). That requires 2 cubic inches per count, so 22 cubic inches. You'll have to look in the box for a cubic inch count stamped into it.