1. I dunno if you mean artwork or animation, but I'll assume both. Artwork is a rare thing for me to be drawn to (Mushishi's probably the only series to do that to me). Animation, on the other hand, I've watched quite a few series specifically for the animation (i.e. Highschool of the Dead).
2. It's not really what draws me in most of the time, but it is the thing I'm most critical of when I watch it. I can't stand when major plot points are left unresolved or there isn't a solid conclusion, but that said, there's a lot more possibilities with storylines in anime than there are films or TV shows, which I do enjoy.
3. This is usually the thing I look for most when I go in. I don't get attached to them very often, but as a writer, I do enjoy complex and well-written characters, plus I enjoy all the strange quirks anime casts usually have (i.e. physical deformities, bizarre attitudes, etc.).
5. Not very often. I'm not really into the typical shōnen superpowered fights like in DBZ or the Big 3, even FMAB which I actually enjoyed watching. Great gun and swordfights, though, I love watching, as long as they're well animated.
Other than those, I also seek out series that are known for having a good English dub. It's the reason I watched Black Lagoon and Yu Yu Hakusho.