The ban on melakha after midday on Erev Pesaḥ applies to full-fledged work that people typically do for a living, such as sewing, building furniture, and planting saplings. However, one may cook, clean the house, or travel before the holiday. As a rule, the ban on melakha on Erev Pesaḥ is similar to the ban on melakha during Ḥol Ha-mo’ed, and in certain cases is even slightly more lenient. Therefore, everything the Sages permit on Ḥol Ha-mo’ed is also permitted on Erev Pesaḥ.
There are three types of melakha: melakha gemura (full-fledged melakha), professional repair work, and the simple work of a non-professional. Melakha gemura like sewing garments, building furniture, and cutting hair, is always forbidden, even if it is done for free. However, mending clothes, even if it demands professional expertise, is not considered melakha gemura. Therefore, if the mender receives payment, it is forbidden, but if he works for free and the mending is needed for the festival, it is permitted. Simple work like sewing a button, if needed for the festival, is permitted even for pay on a temporary basis. It is likewise permissible for one to summarize his ideas in writing as he studies, but if he earns a living from typing or copying, it is a melakha gemura and thus forbidden (SA 468:1, 2).
Though it is forbidden to have one’s hair cut after midday on Erev Pesaḥ, it is permitted to shave with one’s own shaver, because this is non-professional work. It is likewise permitted to iron clothes, shine shoes, and cut fingernails after midday in preparation for the festival. However, some are stringent to shave and cut fingernails before midday.
As noted, all melakhot permitted by the Sages on Ḥol Ha-mo’ed are also permitted after midday on Erev Pesaḥ. These are the five instances in which melakha is permitted on Ḥol Ha-mo’ed: 1) skilled labor, for pay, to address personal needs, primarily the preparation of food for the festival; 2) non-professional work for pay or skilled labor for free, for other festival needs; 3) melakha for something fleeting, to prevent substantial loss, even by a craftsman for pay; 4) melakha done for public benefit or for the sake of a mitzva; 5) melakha performed by a poor person who lacks the money to buy festival necessities (Peninei Halakha: Festivals, chapters 11-12).
I did not mention laundering even though it is listed as a melakha gemura in SA, since nowadays laundry is done by machine and might be considered non-professional work done for the sake of the holiday, as stated in SSK ch. 42 n. 139. Laundering is permitted on Friday after minḥa.
. MB 468:5 states that preferably one should cut his nails before midday, although many permit one to cut his nails even on Ḥol Ha-mo’ed (SA §532 and Ḥazon Ovadia vol. 2 pp. 89-91). She’arim Metzuyanim Be-halakha 113:6 also permits polishing shoes. According to R. Mordechai Eliyahu (Kitzur SA 113:5), one may shave even after midday, although it is better to shave before midday.
If one forgot to get a haircut before midday and his appearance is not appropriate for the holiday, he may get his hair cut by a gentile, since the ban on work applies only to Jews. Even though the Jew getting his hair cut helps the gentile do his job, it is permissible so that he will have his hair cut for the festival.