My father passed away last week and was buried on 20 March 2020. The Shiva has just ended and the Shloshim would usually end on 18 April (I think) which is just after pesach.
Question 1) does the shloshim finish on erev pesach?
Question 2) under these circumstances when is it permissible to get my hair cut, shave and cut my nails?
You are correct, the shloshim finishes on Erev Pesach. After midday you can cut your nails and bath, however regarding shaving and taking a haircut, since you are mourning a parent, things are different. A mourner abstains from taking a haircut until his friend would reprimand him that his hair is too long.
O:CH 548-9, Y:D 390-4, 399-3,Tziyunei Halacha pg. 392,