Yes. On ice is preferred for up to four days.
No. Shrimp that has been left out overnight is not OK to eat.
Sure... but it will more then likely be over cooked. Shrimp does not take long to cook. Your shrimps texture may be a little tough. But YES, you can fry pre-cooked shrimp.
about a week
Cooked pinto beans are considered potentially hazardous. They should not be left unrefrigerated for more than 2 hours.
Probably not - hot foods should be either kept hot or placed in the refrigerator within 2 hours of cooking.
Shrimp cocktail is not cooked, though the shrimps will be par boiled and cleaned before you add your sauce
no
Only a few hours, then dispose of them..
According to the Clemson University Extension article "Safe Handling of Seafood" cooked shrimp stays good in the refrigerator for 3-4 days.
That depends how long they have been unrefrigerated. If they've been sitting out for more than 2 hours, I wouldn't use them.
The recommended amount of shrimp per person is 1 pound of raw shrimp or 1.2 pound of cooked. For 60 people you would need 60 pounds of raw or 30 pounds of cooked shrimp.
It's not a good idea. Shrimp don't have much of a shelf life anyway and they will probably turn mushy.