The thing is, we really don't know much about the background of the Inquisitor will be at all at this point. They haven't released the pre-created backgrounds yet, so how can you determine that so easily so quickly?
I think it's too early to tell whether or not the Inquisitor would be Varric's type. Also, he certainly would not have found a couple of my Hawkes his type at all. I think that's pretty subjective depending upon how someone played his/her Hawke.
It's not so much who the Inquisitors were but more who they will become. When has Varric ever wanted to be the center of something rather than just more of an observer? With Hawke, they at least tried that but the world had different plans while the Inquisitor will be the head of an organization that will be in everyone's radar and possibly crosshairs.
The first one is a personal issue with you only, if you can't get over that it's ok. Varric just isn't for you.
The second one is gonna be an issue with someone no matter what, Varric or otherwise. But an earlier post in this thread gave some reason why he might be gated against Qunari.
The third one is really just speculation, we don't even know what the Inquisitor is like.
See, I'm already uneasy with how he is going to be judging Iron Bull for something he didn't do and is only connected by affiliation. If that extends to all Qunari including our Vashoth Inquisitor, then sorry to say but Varric is a racist. I don't like racists.
True, but I'm sure Bioware will write it in a way that doesn't seem like that
Racegating will imply that either way. Does it matter whether it's Varric, Vivienne, Blackwall or Solas that gets racegated for "racist" reasons?
Why do you think Hawke was more his type? Doesn't it depend on how you play Hawke and how you play the Inquisitor? I'm pretty sure if you played Hawke as an aggressive asshat then Varric wasn't into that 
There's no time gaps like in DA2, so I don't see how.
As for the bottom parts, I kind of answered in the upper two parts of this post.