what is the name of the hand position in this? -are there any restrictions for who can/cant say this and where/when?
ב"ה Shalom' I am not aware of any special name for this, besides referring to the positioning of the fingers as 5 "Charachim", meaning 5 open spaces between the fingers. The Priestly blessing is said only by "Cohanim" who are those who have lineage being from a priestly father. Jews who are not from priestly descent are forbidden to carry out the priestly blessing. Since the Cohanim are required to lift both hands when conducting the blessing, there are those who express reservations to using both hands when blessing their children on the eve of Shabbat. However, many have the tradition to use both hands. All the best