It would depend on a couple things.
1. time of day the check would be deposited
2. bank the check is drawn on, and the bank that Publix uses. If they are the same, clearing would happen as early as saturday.
As long as #2 doesn't come into play where both are at the same bank, then clearing wouldn't happen until monday.
No
You can cash it at your bank, or check cashing retail store. Check your phone book or Google search check cashing with your city name. (i.e check cashing Orlando)
http://www.helpwithmybank.gov/faqs/banking_check_cashing.html offers information on the regulations of, and laws behind check cashing.
Deposit in your account or a check cashing place will do it for a fee
Most banks charge nothing if you have a checking account with them. Grocery and convenience stores usually charge a percentage (~3%) for business check cashing.
The account holder does not need to be present when the check is cashed.
You might be better off going to a bank and cashing a check, since they can verify that there is money in the account and a gas station can not. No banks offer check cashing cards anymore.
To cash a personal check drawn off your banking institution you will need to have a valid drivers license. You will need to to endorse the back of the check. Funds will be verified and your check will be cashed.
Some of the more popular check cashing locations will vary by city, but Walmart, Check N Go, The Check Cashing Store, and Speedy Cash are some popular check cashing locations.
No Publix does not "hold" any paychecks. The pay period ends on Friday night, and you are paid the following Wednesday-Friday, depending on your preferred method of delivery; that is, direct deposit in the credit union, a bank, or a paper check.
You can cash a check at a check cashing agency on Labor Day. Walmart will also cash your check as long as it isn't a personal check.
Go to a bank or check cashing place. You wil be charged a fee with the check cashing.