Does it have collection support

There's Wabbajack. But I don't use collections as a lot of the modding community has some really weird preferences. There's tons of mods that a lot of collections use to make Skyrim more like Ubisoft games, which personally makes me mentally gag to think about.

and can you download mods from in the app?

I didn't know this was a thing and I honestly don't get why this would be an advantage over just using a browser. I often compare multiple similar mods before picking one to add, and I don't see how Vortex could beat a browser for that.