Is there a restriction on shaving or cutting of hair (head, facial, or pubic), and clipping of nails, during any part of the first 10 days of Dhul-Hijjah (Zilhij)?

It is Mustahabb (preferable) to fast on Friday corresponding to 9th of Dhul-Hijjah. Refer below

and Allah Ta'ala Knows Best

Moulana Imraan Vawda
FATWA DEPT.

CHECKED AND APPROVED: Mufti Muhammad Kadwa

SIGNIFICANCE OF THE FIRST TEN DAYS OF ZUL-HIJJAH
. Ibn Abbaas (Radhiyallaahu Anhu) relates that Rasulullah (Sallallaahu Alayhi Wasallam) said, 'On no other days are good deeds (Amal Salih) more liked by Allah than on these days - meaning the first ten days of Zul-Hijjah'. The Sahaab asked, 'Oh` Rasulullah! not even Jihaad in the way of Allah?' Rasulullah (Sallallaahu Alayhi Wasallam) replied, 'not even Jihaad in the way of Allah, except for that person who goes out to fight with his life and wealth and does not return with anything'. (Bukhari) . Rasulullah (Sallallaahu Alayhi Wasallam) says, 'on NO days is the worship of Allah desired more than in the first ten days of Zul-Hijjah. The fast of each of these days is equal to the fast of a whole year, and the Ibaadat of each of these nights is equal to the Ibaadat of Laylatul Qadr'. (Tirmidhi and Ibn Majah)
. Abu Qatadah Al-Ansari RA relates that Rasulullah (Sallallaahu Alayhi Wasallam) was asked about the Sawm (fast) on the day of Arafaat (9th Zul-Hijjah). He said, 'It compensates for the minor sins of the past year and of the coming year'.
. Rasulullah (Sallallaahu Alayhi Wasallam) has said, 'the most acceptable Du'a is that which is made on the day of Arafah, and the best Du'a which the Prophet`s before me and I have said is:
Laa Ilaaha illa llaahu Wahadahoo laa Shareeka lahu, Lahul Mulku walahul Hamdu Wa Huwa Alaa kulli shay en Qadeer.
. It is related from ibn Abbaas RA that Rasulullah (Sallallaahu Alayhi Wasallam) said, 'no days are as weighty with Allah and so liked by Him for good deeds than the first ten days of Zul-Hijjah. So in these days increasingly read TASBEEH (Subhaanallah), TAHMEED (Alhamdulillah) and TAKBEER (Allaahu Akbar). (Tabraani).
It is related that Rasulullah (Sallallaahu Alayhi Wasallam) said, 'Whoever stays awake and makes Ibaadat on the nights of Eid-ul-Fitr and Eid-ul-Adha, his heart will not die on the day when all hearts will be dead'. (Targheeb).