I turned it upside down and it has now calmed down. But how long will this save last?
Until the bearings on the opposite side wears out. Not long usually.
I am terrified of (a) losing my back-up inside if the fan is lose
A dead fan will bring up overheat error and you should then stop using the TC and pull the hard disk. You can recover the backup from hard drive. Of course backups are not usually a major issue.. more important is you have not copied files to the TC which are deleted from the Mac.
You can replace disk in the TC as well as the fan.. or better still scrap the whole thing and buy a local usb drive for backup. Plug it directly to computer and start a new series of backups.. today.
(b) trying to buy a new time capsule and set my system up again with the router,
Apple stopped making Time Capsule 3 years ago and they are unsuited to the latest Mac OS.. it is time to move on.
How do I save my backups inside the squeaky box?
The Apple method.
Plug a 3TB or larger Mac formatted USB drive into the USB port of the TC.. go to the disk tab in airport utility.. select archive.. and give it a couple of days to backup.. No backups can happen while this is archiving.
The non-Apple way.
Stop using the TC NOW.. pull out the hard drive and plug it into a USB dock or enclosure for drives. Copy the backups to other suitable location if necessary but likely not needed.. better start using the USB dock etc to backup the Mac directly.
Or if you wish to continue doing network backups..
A NAS such as Synology.
Some routers with USB3 ports like Asus or Synology will work
If you have a desktop computer recent model running big sur or maybe catalina it can host a large USB drive for network backups. Or buy a second Mac Mini after 2012 model and use it with at least Mojave or even Big Sur on later one as backup device.
Apple, how could you let me down like this?!
If this is your first experience of Apple leaving their users high and dry.. you have much to learn young paduan.
The correct response is Yes Sir.. No Sir.. and very quietly.. 3bags full Sir!! I will leave it to your imagination for what the bags are full of.