The fan belt fell off and the a/c climate part mented the belt so is that part going out

wow old and still on the road that old, rare here, USA.
the charge lamp means the Aternator is failing
causes are.
1: belt slips to it or belt missing
2: wire to it fell off. or burned, cut etc.
3: fuse huge 50amp blown under hood.
4:the alternator is bad.
5:engine trouble such that RPM is 500 rpm AT IDLE AND THE ALTERNATORS JUST DO NO LIKE THAT.

ALL YOUR STATED EVIDENCE IS 100% NORMAL FOR DEAD ALT.

charge up the battery and drive to a shop and tell them to fix the ALT.
they even test it.

Sorry Graham, it is based on a Buick, the big difference is your 3.8 does not have a distributor at all, no where for it to go even, you have to start with your fan belt using a 3/8 drive bar that fits into the flexible belt tensioned, then remove ALL the plastics from the front of your engine, the water pump is under them, not a nice job so I would look at replacing any belts bearings and seals as you go

they allways runnnnnnnnnnnnnn.not to worry.

You may have a idler or pulley that is getting a bad bearing and throwing the belt. The belt can stretch some but if they do most will squeak or not cool the engine and you will see the engine temp go up when it is slipping and then when it catches the temp will go back down.

go with japanese and no climate does not effect the life span of belt

The A/C compressor has its own belt and tensioner. The alternator, p/s pump, and water pump use the other belt and tensioner. Make sure you check the A/C belt while you're digging around in there. If it is cracked replace it.

I’m happy to assist further over the phone at https://www.6ya.com/expert/jeremy_d728a59f986299fa

assuming you have the 3.3 engine

no,if your belt is still good

The fan assembly is attached to your water pump i believe the bearings in the water pump have failed ,causing the whole fan to move up and down, that is what through the belt best of luck to ya :)

I would go with a fan motor, but would like to see this myself first.