A west facing window can heat up in the summer. As well, the light refracted through the glass may make for an even more intense growing place. Sage, rosemary, thyme and oregano may be able to handle the light and heat--they have the skins equipped for it. The tissue of the chives, dill and basil may be a bit thin (and these may prefer a bit more water than the others). You could experiment this year to see which ones succeed.

If you're growing indoors, your zone isn't nearly as relevant as when you're growing outside.

The cat thing is tricky. I've had some luck putting things in a place that the cat won't view as stable. It also helps if the diameter of the plant isn't very different than the diameter of the pot, so there isn't a big expanse of tempting dirt, beckoning to be used as a litter box. You could also consider some sort of less-tempting soil covering, like decorative stones or moss, which might also help you with moisture retention in the desert.

Posted a deterrent for keeping cats out of the plant area. Its within a recent thread here. They hate walking on prickly spikes like birds do.

while the cat jumped up on the rim of the container....so i dont really think that will do anything so now i went down to lowes and bought sage,oregano,lemon thyme,and prostrate rosemary and because of the cats i put my plants in a tinted room with a grow light and now my sage is dying and its a desert plant so i dont give it a lot of water maybe a 1/8 of a cup of water a week...i'm trying to simulate what is like outside....????what am i doing wrong i got it in a 6x8" pot with an oregano plant?????