From the 2002 General Instruction of the Roman Missal (GIRM) approved for the USA, which can be accessed from
romanrite.com/girm.html :
“154. … The priest may give the sign of peace to the ministers but always remains within the sanctuary, so as not to disturb the celebration. In the dioceses of the United States of America, for a good reason, on special occasions (for example, in the case of a funeral, a wedding, or when civic leaders are present) the priest may offer the sign of peace to a few of the faithful near the sanctuary. …”.
Regarding people going into the sanctuary:
“294. The People of God, gathered for Mass, has a coherent and hierarchical structure, which finds its expression in the variety of ministries and the variety of actions according to the different parts of the celebration. The general ordering of the sacred building must be such that in some way it conveys the image of the gathered assembly and allows the appropriate ordering of all the participants, as well as facilitating each in the proper carrying out of his function.
The faithful and the choir should have a place that facilitates their active participation.[footnote 114. Cf. Sacred Congregation of Rites, Instruction Inter Oecumenici, on the orderly carrying out of the Constitution on the Sacred Liturgy, 26 September 1964, nos. 97-98: AAS 56 (1964), p. 899.]
The priest celebrant, the deacon, and the other ministers have places in the sanctuary. Seats for concelebrants should also be prepared there. If, however, their number is great, seats should be arranged in another part of the church, but near the altar.
II. ARRANGEMENT OF THE SANCTUARY FOR THE SACRED SYNAXIS (EUCHARISTIC ASSEMBLY)
295. The sanctuary is the place where the altar stands, where the word of God is proclaimed, and where the priest, the deacon, and the other ministers exercise their offices. …”
From the footnote 114:
“98. Special care should be taken that the places for the faithful will assure their proper participation in the sacred rites with both eyes and mind. Normally there should be benches or chairs for their use but, in keeping with the Constitution art. 32, the custom of reserving places for special persons is to be suppressed.
Care is also to be taken to enable the faithful not only to see the celebrant and other ministers but also to hear them easily, even by use of modern sound equipment.”