Can I use multiple partition external HDD connected to Apple Airport Extreme for Backups from both Mac and Windows PC
According to the Apple support article
https://support.apple.com/en-ca/HT202807

The disk must be formatted as Mac OS Extended, FAT16, or FAT32.
...
AirPort base stations don't support encrypted formats or disks formatted as APFS, ExFAT, or NTFS.

So, unfortunately, it seems like the the answer to your title is no, at least for the Windows / NTFS portion. However, since Time Capsule and AirPort share HFS+ over SMB - any client can write to the disk if you just format all of it using one of the supported file systems (Mac OS Extended, FAT16, or FAT32).