How much will inquiry raise my score

Credit Karma might have a simulator.  The credit bureaus may also have simulators, you can make a free account to log on and you get some benefits although they will try and sell you on more expensive services.

Just the inquiry to see if you are credit worthy will drop you a few points, if the lender does a "hard" inquiry.  If the lender does a soft inquiry, it won't affect your score.  Opening a new card will lower your score at first, but it will bounce back and should go higher if you only use it sparingly (your debt as a percentage of total credit available to you goes down when you open new lines).  I have a feeling it will be more than 8 points though, at least at first.