First off, this is the hardest lesson I have tried to learn in entirety on GMC:

Using the guitar pro file, on measure four (the sixteenth note triplets) do you economy pick this or have another method of going at it?

I can play licks like this fairly well when acscending but this descending pattern is giving me just a little trouble while staying in rhythm

That's a combination of picking and pull offs. I guess I am picking as I would normally alternate pick it except that I miss the notes that are pulled off. You can do your own way as well but pull offs ARE important

Maybe this would be more clear in a video; but, normally I come at the strings with and angle on my left hand (Kind of like Slash or Jimmy Paige would) but when you are executing legato, is it better to come at the strings more vertically? I think I remember saying pulls offs are easier when you raise hand and use more of the tip of your finger?

Yes, that's what I do a lot. Tip of the finger is the way to go and pull off hard to be heard almost like a picking.