Targeting the same spell on stack
Yes, this is fine.

Remand will counter Grapshot and move it to its owner's hand. Then, when it comes time for Negate to resolve, it will be countered by the rules instead (for not having any legal targets).

It's worth noting that Negate is particularly ineffective against Grapeshot as it will not stop the copies from being made even if it counters the original spell.