Just becauase you dont see weather cracking doesnt mean the tire is safe. Tires should never really be used or kept outside for more than 4-6 years depending on the geographic location, in places like michigan or florida you're looking closer to the 4 year mark where they start becoming a risk, more moderate locations like kentucky are closer to the 6 year mark.
You have to remember, you usually cant see the worst of the tire, right in the bead is usually the worst spot on a tire. Most tires I pull off that are 4+ years old are cracking in the bead, even if the rest of the tire looks fine. If you're not sure of the age, there is a date code on one side of the tire right after the DOT number.
The rim is fine as long as you didn't put a huge gash in it. If you did, just go buy a 16in steel rim from a junkyard and put it on. Just a couple things to note about used rims. Always check the size of a 16in rim with a go/nogo gauge, mounting a 16in tire on a 16.5in rim can kill the person mounting it or anyone else standing beside it when it does explode (the shop should always check with a go/nogo gauge when putting a tire on a 16in rim that came in without a known fitting tire.) If you're unsure any tire shop will have one and check for you. Or you can measure with a flexible tape around the edge of the rim, 16in rim will have a circumference of 50.25in and a 16.5in rim will be 51.8in.