Corn is okay for tiels, its actually good for them. My tiels LOVE corn! I usually give them the canned one, which is boiled corn. They LOVE it! Since you have wild bird seed, do NOT give it to the tiels. Wild bird seed may have certain things that are not meant for pet birds, and it may not be good for them. Leave the wild bird seed to the wild birds. All bird seed is NOT the same. LOL Your wire cage sounds like its spacing is too big for a tiel, which can be dangerous. As for doubling its wires, that's not recommended for birds, because it can be hazardous to their safety. I would recommend buying a new cage made for cockatiels, because rat cages are made for rats, not birds. The cage should have a tray at the bottom on which you can put a sheet of newspaper as their litter. The spacing should be 1/2-3/4 and inch..........no more, and no less. There should be at least two sides with horizontal bars. Cages with all verticle bars are fine as long as they have a horizontal bar going after about 5-6 inches or so. If there are no or too few horizontal bars, the bird can have difficulty climbing. The cage should be at least twice the wing span of the bird in width, and twice-3 times the length of the bird (head to tail) in height. It should be made of sturdy, non-toxic material, and preferably made for birds. You can find wonderful bird cages at almost any pet store, and they are usually made to look pretty also. Personally I wouldn't use a rat cage for a tiel, but is it possible that you can post a picture?
I've never fed my tiels Hartz so I don't know much about it. I feed them Kaytee and Zupreem, but recommended by my avian vet.

My birdies' favorite salad consists of broccoli, peas, cauliflower, corn, and carrots. Not oils/juices added. They LOVE it!