Should a radiator be loose

Do not drive this vehicle! Sounds like your wheel bearing assembly is loose. If it's the cover behind your rotor, you may lose your entire wheel. If you can jack up the rear, wiggle the tire by placing your hands in the 3:45 or 9:15 position according to a clock. If you have any wiggle left to right or up and down expect a bad wheel bearing assembly. If not, it could be loose.

first order of business is to see if your leaking, best bet is to start it up and pop the hood, look at fittings and connection, look under the car to see if you have a drip. likely areas are back of water pump, radiator seams, hose ends&connections. look for damaged or cracked & brittle hoses as well. chances are its leaking the water somewhere. if its not leaking then its loosing it because its boiling over when you over heat. if this is the case its either your water pump, thermostat, cooling fan or radiator. you can check your water pump by looking at the weap hole under the pulley and see if its leaking water, or by removing the belt and wiggling the pulley, if its loose or wiggles around the bearing is shot, if it seems good and tight then you should be ok. you can test your thermostat by removing it and placing it in a boiling pot of water and see if it opens up, you can check you fans by simply starting the car and letting it get to operating temperature and seeing the the fan turns on. and you can check you radiator by taking it to a radiator shop and having it tested.

Usually not, most GM cars that use a link from the top of the engine to the radiator core support have engine/transmission mounts that support the weight of the engine and transmission. The mount you describe sounds like a torque rod, there to control the torsional twist of the engine. Try loosening the bolts to this unit, if it will wiggle by hand it probably isn't bearing a load.

loose wires at computer

yes its a big concern as if that belt comes off it will do internal motor damage that is very expensive to fix. First by hand pry the belt over and turn motor over by hand and get the belt back on the grooved pulley. it is possible you have a bad idler pulley or a tensioner pulley. both have bearings in them and they do wear aproximately every 60 to 80 thousand miles but it sure seems like its alot more. those pulleys run about $ 80.00 depending on what tensioner you have and where you buy them from. also replace that belt at this time,since it has sliped or rode in a bad spot it most likely is wore, stretched, or twisted, and you do not want to tear down and fix twice, once is bad enough

there are rubber boots on the bottom that the radiator has to go in and those boots go in holes in the core support. if your trying to drop it in there. take it in at an angle, drop the right hand in first then start moving the lines out of your way as you lower the other. jst wiggle it in there. you can do it.

Wiggle radiator out towards motor and up. Remove air breather box if you haven't already. Been there, done that.

No it sounds like you have a bad water pump..

Try taking out the thermostat and putting in a cup of hot water then see how fast it opens ,then in cup of warm water and check again then add hot slowley and if doesent open and more get a new one.
Also check the Radiator after running when temp is almost at usual working temp and turn engine off and now check radiator by putting your hand flat on the core all over and if you have hot and cold spots then the radiator could be bunged up or dirty inside and out side in the fins(use garage compressor to blow out dust),
If still gets hot check to see if you are loosing coolant if so have the engine checked A Compression test as you might have compression getting into the water system due to head gasket ,but check all above first.
Let me know how you get on ... RON

sounds like a wheel bearing