I have a friend that attends an SSPX chapel. Would I be able to attend Mass with her and receive Communion? Do these Masses fulfill one’s holy day obligation?
There is some degree of disagreement over whether or not Catholics should seek to fulfill their Sunday/holy day obligation at an SSPX chapel. Some in the hierarchy have said that attendance can fulfill the obligation, but have advised Catholics against attending. There is certainly no need for a Catholic to attend an SSPX liturgy so as to fulfill the obligation—even if there were no other Mass available (which is practically never the case), a Catholic would simply be dispensed from the obligation to go to Mass that day.
I cannot recommend that you attend these liturgies with your friend, especially if your friend is attempting to draw you into joining her in her support for the SSPX and her refusal to attend liturgies licitly offered by priests in good standing with the Church.
As for receiving Communion at an SSPX chapel, I cannot ordinarily recommend receiving Communion from an SSPX priest. The SSPX have been given faculties by Pope Francis to hear confessions during the Jubilee Year of Mercy (2015–2016), but beyond that they do not have permission to celebrate the other sacraments (including the sacrament of the Eucharist).
If you are interested in attending a Mass offered according to the extraordinary form of the Roman rite, I recommend calling your diocese and asking for locations where it is licitly celebrated in your area.
Vatican II and its changes