Does the UN still recognize the borders of the 1947 Palestine partition?
The term "recognition" in the context of the UN is normally concerned with membership of the UN general assembly. I interpret your question as concerning the continuing validity of the resolution, in the view of the UN general assembly and international court of justice.
Yes. The 1947 plan (Resolution 181 (II)) is still regarded by the UN as applicable in the 21st century.
This seems to be covered by the relevant Wikipedia article
A General Assembly request for an advisory opinion, Resolution ES-10/14 (2004), specifically cited resolution 181(II) as a "relevant resolution", and asked the International Court of Justice (ICJ) what are the legal consequences of the relevant Security Council and General Assembly resolutions. Judge Abdul Koroma explained the majority opinion: "The Court has also held that the right of self-determination as an established and recognized right under international law applies to the territory and to the Palestinian people. Accordingly, the exercise of such right entitles the Palestinian people to a State of their own as originally envisaged in resolution 181 (II) and subsequently confirmed." In response, Prof. Paul De Waart said that the Court put the legality of the 1922 League of Nations Palestine Mandate and the 1947 UN Plan of Partition beyond doubt once and for all.
The references given were
 See paragraph 5, Separate opinion of Judge Koroma
 See De Waart, Paul J.I.M., "International Court of Justice Firmly Walled in the Law of Power in the Israeli–Palestinian Peace Process", Leiden Journal of International Law, 18 (2005), pp. 467–487
Judge Koroma specifically wrote
- The Court has also held that the right of self-determination as
an established and recognized right under international law applies to
the territory and to the Palestinian people. Accordingly, the exercise of
such right entitles the Palestinian people to a State of their own
as originally envisaged in resolution 181 (II) and subsequently confirmed.
The Court has found that the construction of the wall in the Palestinian
territory will prevent the realization of such a right and is therefore a
violation of it.
Articles 10 and 14 of the UN Charter refer to General Assembly resolutions as "recommendations"
Also, does the UN still consider Jerusalem corpus separatum?
I would like to know in particular which UN resolutions superseded the 1947 partition.
With a subject of this complexity I believe it is best to ask separately.
See One post with multiple questions or multiple posts?