CSIDH Squaring Fixing the Base Curve
If you have a solver for P1, then it can also solve P2, so the problems are comparable: P2 is easier.
P1 is assumed hard, and is used as the basis of, e.g. https://eprint.iacr.org/2020/1012.
P1 is known to be generically equivalent to P3 (see https://hal.archives-ouvertes.fr/hal-02373179 and https://eprint.iacr.org/2020/1012), however P2 is probably not equivalent to P4: the reduction does not work for these more constrained problems, and P4 is known to be easy, whereas P2 is likely not.