IIRC, Seven of the nine current members of SCOTUS have recognized their subpoena power.
Technically, yes.
The House rules allow for the Speaker of the House to create special "select" committees. It is customary, but not by rule, to allow the minority leader to appoint the minority members, but the rules for these special committees allow the Speaker to have the final say.
In this case Pelosi was exercising raw partisan power here, because McCarthy appointed Jim Jordan to the committee. Pelosi knew that Jordan would be a strong opponent of the tactics that Pelosi was setting up this committee to perform. To ensure her wishes, Pelosi rejected McCarthy's nominees and she named the Republican members herself, grossly against custom by not against the rules.
So, calling this committee illegitimate is a partisan political play, but not a Constitutional one.
-PJ