I’m opening up a Indian restaurant in Northern Ireland, would the spice girls be a good name for it?

It might if you were to use capitals for: The Spice Girls.

spice grills would be a better choice perhaps? Or spicy schits.?

You don't want to sound like a night club.

I’m opening up a soul food restaurant in China, would Public Enema be a good name for it?

Curry Blast! would be a good name 

No. Indian society is very male oriented. Naming a restaurant anything "Girls" would be viewed as an insult to men And therefore unacceptable.

How about just "Spices"

if you have no problem handling criticism than it a good name

You're in Ireland, I would use a name that is appropriate for those Irish people are prone to cutting people heads off over offenses.

That name you've chosen seems clean but could associate itself with the band spice girls which Irish people would consider taboo and they would enslave you in their castle and cut your head off.

You can use that name at your own risk, in the USA you can use any name because we don't cut peoples heads off over everything

Sharty Spice Runs

Only if it is going to be staffed with talentless 40 year old women.