Used car buying advice wanted

So I totaled my girlfriends car a few days ago and need to get her a new one. Luckily after the deductible, the insurance company is giving us a check for $10k. I want to make sure the car is at the very least comparable to her 2009 Toyota Camry (65k miles), but preferably something newer or similar in mileage but better. The Camry didn't handle to well in the snow and ice, so maybe something with AWD. My absolute max budget with the insurance check is $16k. 

 I've only purchased cars opportunistically from friends and family in the past, so this will be my first time dealing with car salesmen. Hopefully you can answer some of my questions:

1.) How far below the sticker price is it reasonable to make an initial offer on a used car? My gf really likes this car listed at $18.5k online, but that is $2.5k over my budget. If I can't find another of the same car for much less than $18.5k would it even be worth visiting that dealership and making them an offer more than $2k below their asking price (which is already listed as a "managers special").  

2.) Are financing terms usually better from banks or dealerships?

3.) I'd like to put $10k down no matter what, and finance the rest. How coy should I be with the salesman about this? I've heard that if the salesman knows you're going to use their financing, they're more willing to be flexible on the price of the car. But I also don't want them to know what my down payment is going to be until we have an agreement on the final price.

4.) Is it necessary to have a mechanic come along if buying a car with less than 60k miles? I don't have any mechanic friends in the area  Should I stick to a "certified" used car if i'm not bringing a mechanic.

5.) Any thoughts on the Buick Lacrosse, Cadillac CTS, Audi A4, and Mercedes Benz C-Class vs a similarly used Toyota Camry? These are all AWD, my gf loves them, and I've seen them selling with 60k miles or less for $12k-$18.5k.  

Thanks, any other thoughts on buying used cars from a dealership appreciated. Not really interested in buying from a rando on craigslist or ebay.