1. Have the liberated states formally delegated Russia to continue the USSR's membership in the UNSC?
In fact, the Alma-Ata protocol does explicitly state that the members of the Commonwealth of Independent States agree that Russia should continue the USSR's permanent membership of the UNSC. The agreement is not contained in the main protocol agreement, however, but in an annex to the agreement, which is why you're having trouble finding it.
The relevant article states:
- The States of the Commonwealth support Russia's continuance of the membership of the Union of Soviet Socialist Republics in the United Nations, including permanent membership of the Security Council, and other international organizations.
The agreement, plus annexes, can be viewed in full here. The relevant annex is on page 15 of the pdf.
2. Is there an UNSC Resolution confirming Russia's seat as an UNSC P5 Member in place of USSR? If so, based on what document(s)?
No, there was no UNSC Resolution confirming this - there was a meeting of the UNSC on December 23rd 1991, chaired by the USSR, and then at the next meeting of the UNSC on December 31st, the meeting was chaired by Russia. The chairperson was the same person, however.
Between these two meetings, the representative from Belarus transmitted the Alma-Ata protocol, including the annex above - amongst other documents - to the Secretary-General. This letter is available on the UN website here.
Although there was no official resolution or decision by the UNSC or the UNGA (which was not in session anyway), nor much fanfare - although the representative from Palestine mentioned it in the first UNSC in 1992, saying "this is the first time that the Security Council is meeting with the participation of the Russian Federation in place of the Soviet Union" - the Alma-Ata agreement seems to have been accepted uncontroversially.
The first time the General Assembly met after the change was on February 4th, in a session chaired by the representative from Ukraine. During this session, the change in membership was not mentioned either.
While there was no official acceptance or resolution confirming the change, I think it's fair to say that the membership change was implicitly accepted by the UNSC and the UNGA and stood uncontroversially for at least two decades.