Question

Positive charges are protons. They do not move then how can we be give positive charges to earth?

Answer 1

Charge is carried by electrons moving. The protons are always stationary. The answer I found online is the protons are stuck in the nucleus so they can't move ("strong nuclear force").
The Earth surface is negatively charged. According to the charge-neutrality principle, the electric charge of the whole Earth is ZERO. The reason why the surface of the Earth is negatively charged remains to be clarified. It probably because at the inner core of the Earth, the temperature and pressure is so high that the atoms there are ionized. So the inner part of earth is posstively charged. Therefore, its surface is negatively charged.
earth absorbs negative charge because of difference in charge density (charge per unit area) between the charged body and charged earth. The charge density is always more in the body than in the earth and hence charges always flow from the body to the earth - be it +ve charge or −ve charge.

The low charge density of earth is because of very high area compared to the area of the body being earthed.