Lately when I've gone to tort a cake, the outside of the cake is hard and it tears as I tort it. I use a Wilton leveler, but I have to start it with a knife. Should I tort it while it's still hot or warm or should it be completely cool?

I let mine cool completely. What are you using to grease your pans. Sometimes that can make them "crusty".

I use shortening to grease the pans. But I tried only greasing the bottom, and it still seemed crusty. Is there something better? Or should I be flouring the pans too?

the issue could be the sharpness of your knife as well. blunt knives will take bits of cake with them.
xx

I'm using a Cutco serrated knife, so I'm pretty sure it's not dull.

Before torting your cake, make a shallow cut around the cake only. I do have the wilton leveler but went back to knife and floss for round cakes and to knife for rectangular cakes.

Make a cut around your cake - to cut the crust only. This avoids the tearing as you cut.

For a round cake, take floss between your hands, lay it around the cake and cross it on the other side. Pull the floss and you get an easy cut.
For rectangle cakes, make the shallow cut around your cake as well and cut the cake after this.

With a bit experience it is as fast as without the cutting around - you can use it as guide and don't need to be as careful as without.

Srsly, you need an Agbay.

Have you checked you oven lately to see if the temp is right? It sounds to me like you are over baking them a bit. Do you use BES (of any sort)?