Can a Time Machine drive have several partitions, or does Time Machine need the whole HDD to itself? Is it possible to partition and external drive an use only one of the partitions for a Time Machine backup?  Or does Time Machine need its dedicated hard drive?  (I've never used Time Machine before.)

If it is possible to do this, do I need to pay attention to anything in particular to make sure it'll work without issues?

I am aiming for one Time Machine partition and one NTFS one on the same external hard drive.  Is this feasible?
Time machine doesn't care what else is on the destination drive as long as the volume (partition) you choose meets the minimum requirements. If the volume you select isn't formatted properly, Time Machine will offer to erase and reformat the part of the drive that will contain your backups.

You might want to try resizing partitions using whatever tool you want before you start accumulating a lot of Time Machine data in case you want to be able to adjust the size of the partitions down the road, but that's more of a problem with partitioning and not something that Time Machine causes.