1. Does Google factor in overall site traffic in rankings? So for 2 sites, all other things being pretty much equal, the one with higher traffic will be listed higher?
I have not heard that google will give you higher positions for having higher traffic. HOWEVER, with personalized search turned on, if a searcher has visited your site before it might receive a higher position in a SERP.
**2. Does this logically imply that sites with lower traffic overall face an uphill struggle to be ranked highly??? **
Holding the high ground is always valuable. If you have a site with a LOT of traffic that is a LOT more people who might link to you, like you, tweet about you, etc. The site with the high traffic has a huge advantage. Some sites receive thousands of likes and tweets, etc every day!
3. As an extension to this, would it be true to say that by increasing site traffic, say with Google Adwords or other online or offiline or whatever advertising, that might help get higher SEO rankings???
I don't think that traffic flowing into your site through these other routes has a direct impact on your rankings. However, as mentioned above it is a higher population of people who might link, like, tweet, etc.
You mention "offline"..... if those people type "yourdomain.com" into the google search box or toolbar then that will signal google that people are "asking for you by name". I think that these domain queries have enormous value. I've never heard anyone from google say that they are kickass or any SEOs saying that they tested, but I would bet that they count for a lot.