In the 1962 Missal, in a Solemn Mass the Subdeacon sings the Epistle and the Deacon sings the Gospel.
Since the abolishment of the Minor Orders in the “Ordinary Rite” (The FSSP still has valid minor orders however), there is a certain level a current seminarian needs to act as Subdeacon- if he has reached Tonsure he can wear the maniple- if not he wears the dalmatic only I believe. Any Deacon can fill the role of Deacon, even permanent deacons- find two of them and you have Deacon and Subdeacon- even a priest can perform the “subdeacon” role at Solemn Mass- just remember the ordained can fill lower roles, but a Deacon cannot do the priest’s role, and a seminarian not yet a Deacon cannot do the deacon’s role at Solemn Mass.
Most likely you will not see a “Solemn Mass” for some time in the local “Ordinary Rite” parish, you will simply have Low Mass or a sung Low Mass without Gregorian Chant.
The priest alone does the readings- as was done in 1962 at Low Mass. Lay persons are not allowed to do this- the only lay persons allowed in the Sanctuary also are male altar boys- all must wear the traditional cassock and surplus. Any lay person entering the Sanctuary to set things up must also wear a cassock.
It makes no difference as to the “actual direction” of way the altar faces. There is what is called “liturgical East”…as long as the priest and people face the same direction - that is established. If the pre4ist has some room in front of the current altar he can say Mass there. If not you would have to get a portable altar.