Jeannie, 2 out of 3 of your questions.
Yes! Most companies will enter into contracts with a prospective patent owner if all of their (other) criteria are met. The criteria that they follow prior to this stage (negotiating a patent pending product), will address 90% of the same overall criteria they will use for a "patented product", i.e., a good product is a good product. On the other hand, some companies with aversions to dealing with "pending" patents will state so immediately, and as a matter of policy ( a bad policy I might add).
Yes! I have heard of Big Idea Group. And yes they are a reputable avenue for which to look into . As a matter of fact, I`ve dealt with the president of one of the group`s companies, "Basic Fun" ( Alan Dorfman:15 years ago) . Unfortunately, the prospective licensing deal fell through for acceptable reasons.
I am sure that you can request their standard licensing model. And I suggest that you do so, prior to any meaningful discussions. Good Luck!!!