Will settlers ever toss frag grenades or m. cocktails if they have them in their inventory?

Giving AoE weapons to settlers is a Very Bad Idea.

Giving any explosive weapon to NPCs is always a bad idea. They tend to shoot first - think never, which usually ends in your death. But yes they will use grenades and explosives however they require constant ammo unlike other weapons. Any Big Gun will require ammo although I can't say if the mini gun is listed as one such weapon.

giving explosives to settlers is a hilarious idea. No need for an alarm. just follow the explosions. They are pin point accurate, but entirely reckless.

Yeah, one nuked me when I made the mistake of handing him a fat boy. It's also a bad idea, giving that stuff to companions. They haven't got any second thoughts using them when you happen to stand in the blast radius.