Grandmother was to gift her grand child

"Is this sort of gift allowed? [Grandmother to Grand daughter]"

YES, no tax liability on either.

"Do we require to make a gift deed?"

Confirmation of gift is always better, even if the amount transferred through banking channel.

"Next April onwards my mother wishes to give her grand daughter Rs 150000 as a gift and it will be invested in PPF? Is it allowed without any problem?"

No gift tax liability, but the total amount invested in your PPF account including your minors' PPF acc. should not exceed 1.50 lakhs.

Dear Sir, This is in reference to your reply some times back to my query. As you had mentioned the total amount invested in your PPF account including your minors' PPF acc. should not exceed 1.50 lakhs.
I wish to ask that Can I invest 1.50 Lakhs in my name & 1.50 lakhs in my child's name & combine child's PPF interest into my income? Can I do this? Please clarify, as it seems a bit confusing. Thank you.
 

No. combine ppt balance into minor and your account should not cross 1.5 lakhs. minors income will be clubbed with your income.