As long as you can get the .com, it easy to spell, relatively short enough, and people can pronounce it, and it isn't trademarked or going to infringe on any such issue, you're more than halfway towards an okay name.
http://nomvilla.com/methodology
http://nomvilla.com/case-studies
As far as your specific questions go:
1) The name is the first impression when someone sees the site via other media; i.e. a news article, or word-of-mouth, or an email. It can be the first impression when someone visits your site, but the logo and general design of the site can be the immediate first thing. In either case, the name is in the top 5 things a user first notices, and like a horrific site design, a really bad name can turn off some users.
2) The best possible scenario is an emotional company name with a descriptive product name. Apple: human, small, unlike cold, sterile computer companies of the time. iPhone: descriptive and straightforward. iMac: likewise.
If you don't have a separate company and product name, try to pick something that's in the middle. Don't be overly descriptive, but still try to have the name relate to your company, even in a tangential way.
Here is how i go about finding names:
* Start with a list of nouns/names that you think your product should be called. Put it in a spreadsheet.
* Use a service like http://impossibility.org/ to find domain names that are available and related to your list.
* Keep iterating it over a week/10 day period. I am sure you will stumble upon good names.
Don't over try. Use a codeword till you find a good name. Also, ask for opinions from a couple of people.
Just be sure whatever you come up with is easy to spell and recall. Also, your name strategy should be 'future oriented'. If you should pivot will your name still work? Think ahead of how your product & services may evolve over time.
http://hopperanddropper.com/syllables-scrabble-letters-and-p...
But generally, I would agree that you should just spend some time on it, and move on to focus on building your product and getting it out to market fast to validate your assumptions and business model.
We finally decided that naming the company was too hard and we were just going to go back to our day jobs (I'm exaggerating, but only slightly).
We decided to back-burner it for a day or two, and the next night while I was playing D&D I came up with the name.
If you shout out a few potential names to friends/family - if they start producing random mis-spellings, cross it off your list.
Two sides:
On the one hand, I spent enormous time dreaming up a name for a business. I then registered it with the county, bought the domain name, and blah blahblah. It never resulted in the first sale.
On the other hand, I spent five years working for a Fortune 500 company which has changed it's name twice, once on "a gentleman's coin toss".
The right name has some value (or Bigco wouldn't have changed it) but as others have said you need to worry more about getting customers first.
Best of luck.