I have a time capsule used for time machine and as the primary network for a while. Now I have a new router, and I want to use the TC to extend it.
What is the make and model number of the new router?
What operating system is installed on your Mac?
If you are trying to use the TC to connect to the wireless network provided by the new router using a wireless connection......the TC cannot do this......unless......your new router is also an Apple router.
If you want the TC to extend the network of a new third party router, the only way that the TC can do this is with a permanent, wired Ethernet cable connection between the TC and the new router.
Furthermore, is it possible to create a partition of the HDD to a specific storage?
This is not really practical unless you are a trained technician. To partition the drive inside the TC, you have to open up the TC, very carefully pull out the hard drive, place the drive in a caddy, connect the caddy to your Mac to format the drive, then reverse the process and reinstall the drive back in the TC. Not wanting to do this myself, I asked a repair shop about doing this a few years ago, and was quoted $300-400.