Can I buy a PayPal gift card at a store (yes. Physical Store.) Then add it to my PayPal account balance without needing a bank or credit card?

No, and even if you could, you wouldn't want to. In the event of an income tax audit, you may have to prove that the money wasn't taxable income when it entered your PayPal account, which sounds difficult to do given the source of the funds.

Maybe? They have gift cards for everything else at stores why couldn't they have gift cards for PayPal.

No. ᶘ ͡°ᴥ͡°ᶅ/