A bishop is required to absolve abortion so the question is whether supplied jurisdiction is enough or not (but that is probably what you are asking).

Does the SSPX priests have the authority to lift excommunication brought on by having an abortion? Is it valid when they do that?

Only when there is danger of death.

There are two major considerations, neither of which have an clear answer.

The first is whether or not you accept the new Code of Canon Law.  In the 1917 code, only bishops could lift the excommunication associated with abortion.  In the 1983 code, any priest can.

The second is whether you accept the problem of jurisdiction.  The Church requires clerics to have jurisdiction to hear confessions or preform marriages.  Without jurisdiction, those Sacraments are invalid.  SSPX priests and bishops have been suspended by the NO church, and thus have no jurisdiciton.  If you accept the NO church, you likely have to accept the fact that SSPX priests and bishops lack jurisdiction, unless you subscribe to supplied jurisdiction theory.  If you reject the NO church, then that's an entirely separate issue.

I believe the "official" SSPX interpretation of the matter is that the 1983 code is to be accepted, along with the NO church (in theory, at least), but that SSPX priests and bishops have supplied jurisdiction so that they can hear confessions and perform marriages.  I do not know what, if anything, the Resistance has to say on the matter.

Yes, priests can absolve this without involving a bishop.  Even SSPX and Resistance priests can do this.  Abortion no longer carries the penalty of excommunication.

Don't be troubled over this.  

As much as I dislike EWTN, I think you will find this very helpful: https://www.ewtn.com/expert/answers/abortio2.htm

God bless you.