Can a grandfather gift shares to his minor grand son

"Can a Grand father Gift listed equity Shares to his minor (6 yrs) Grand Son’s Demat Account?".

Yes, why not?

"What is annual limit to Gift in case of a minor Grand Son?"

No limit. depends upon love & affection toward Grandchild AND Capacity of Grandfather

"What will be the Tax implications on the parent/ father of that minor son and also on Grandfather gifting his Shares?"

The taxability will arise only if it is sold. No tax liability over gift, which is tax-free.

Dividend is taxfree; but above 10 lakhs taxable in either of the parent's account whose tax slab is higher.

Date of aquisition will be date of transfer of shares in the register of the company.

Cost of aquisition will be that of the grandfather.