It is permissible to cut nails on erev Shabbos even after chatzos, and even after the time of mincha ketanah if one was unable to do so beforehand (see Mishnah Berurah 251:7). However, one should try and have a haircut before the time of mincha ketanah (see Biur Halachah d.h. umistaprin). Even if one isn’t normally particular to toivel [immerse in a mikveh] on erev Shabbos, this week he should be in honor of the upcoming Yom Tov [see Shu”t Shoel U’Meishiv (Mahadurah 3, siman 123, pg. 21b) who says that nowadays there is an obligation to toivel before Yom Tov as a zecher [remembrance] for what happened at the times of the Beis HaMikdosh, like we count sefiras ha’omer nowadays].
The Shu”t Minchas Shlomah (Vol. 2, siman 35, s.k. 12) writes that one can even toivel on Shabbos, and there is no problem of hachonah (preparing for after Shabbos on Shabbos) when toiveling on Shabbos for Yom Tov, as long as one doesn’t explicitly say that this is the reason he is doing so. Similar, to the Mishnah Berurah (290:4) which says that one may sleep on Shabbos for after Shabbos, as long as he doesn’t say explicitly that he is doing it for after Shabbos.
