First, congrats on owing the greatest grill that Weber ever made! Props to you and your grill.
Many SS Performers came with OPD tanks, and it looks like yours was one of those. The way to remove the tank is to pull back on the collar of the brass fitting on the tank. This is the same connection as a pneumatic wrench or nailer, if you've ever seen or used one of those. Pull the collar back toward the valve on the tank, and the male part of the connection will pop loose. Then you can lift up on the tank to separate it from the hanging bracket and lower it down through the frame.
U-Haul or any refilling station will be able to help you, as long as they aren't confused or alienated by that quick-connect union you have (encourage them to check through their selection of fittings if they seem confused). Your 5-pound tank will hold about a gallon of fuel. The only trouble you might run into is if your tank is older than 12 years (there is a date stamped somewhere on the tank or handle). If they balk at that (they don't always pay attention), you'll need to find a place that will re-certify your tank (for $8-10) for another 5 years. Or you'll need to find an online source or an RV dealership that will sell you a new tank (but these can be very pricey).
Good luck, and welcome to WKC!