How to reformat an external HDD on Mac without losing files?

I need some help regarding macOS.
I’ve got a 2011 iMac that’s still running Lion.
I want to upgrade from Lion to Sierra, but first I need to get an external HDD ready for Time Machine. The drive is currently formatted in DOS, and I have 320 GB of data on it that I can't just move somewhere else and copy back later. (I don't have enough space on my iMac to do that either)
Questions:
1) Is there any way to reformat this external drive to a Mac format without losing all the files already on it?
2) If something goes sideways during the jump from Lion to Sierra, is it possible to get my files back without a Mac? Also, will I actually be able to run my current software, like Illustrator and Photoshop, once I'm on Sierra? That's my biggest worry because I seriously need those programs!!

Can someone please help me out! It's a 1.4 TB WD drive, and it feels stupid to go out and buy a new one just because of this Mac.

Thanks!

If you're planning on upgrading, you really ought to expect some data loss.
It’s basically impossible to format a Mac drive without losing everything on it..

I mean, I always want a backup before any upgrade, just in case things go sideways. It’s just good practice, I guess.
So, what else am I supposed to do besides just dropping cash on a new external drive??

There’s a way to do this, but honestly? It’s a headache. You could grab some partitioning tool, shrink your existing partition on that external drive, carve out some new space from the empty bits to make the partition you actually want, and then shuffle all your data over to it. If you run out of room halfway through—which happens—you’ll just have to delete whatever you moved, shrink it again, and try expanding the other one...

It’s a tedious, long-winded process. I’d say just let it run overnight while you’re asleep so it isn't hovering over your shoulder the whole time.
But there’s a catch—a big one. There’s always a risk. If that partitioning software crashes or if the power flickers—whether it's a freak accident or you accidentally trip over the cord—you’re looking at potential data loss. Beyond just losing files, you might end up with a totally corrupted partition table, and then some stuff is gone for good. No coming back from that.

The easiest, smartest move? Just go buy another drive. Use one as your main and the other as a dedicated backup... you know, just in case one of them decides to kick the bucket.