What are the connotations of "Kadeish Li Kol Bechor"?
Ramban and Seforno: the Mitzvah to sanctify the firstborn
came into immediate effect.
The current Parshah goes on to list a number of other Mitzvos that applied from that time on (See Ramban).
In fact, they became forbidden to perform mundane work until they have been redeemed (as the Pasuk in Re'eh, Devarim 15:19) writes with regard to firstborn animals.
Does this mean that it was only the firstborn of the mothers who died in the plague of Makas Bechoros?
Rashi and Ramban #2 (above, in 12:30): All the firstborn died, both of their father and of their mother, and even the oldest person in the house.
Ramban #1: It was only the firstborn of the mother who died in the plague, as the Pasuk indicates here.
And the reason that the Torah sanctified specifically the firstborn of the mother is because one knows for sure that he is the firstborn, which is not the case regarding the firstborn of the father. See Tehilim, 98:52, which supports this opinion.