Private air charter allows you to access thousands of airports that commercial airlines don’t. Which, in turn, may get you closer to where you are really going thus saving you time and money.

No, it does not. You just show up 5 minutes before departure time (that you select), load, and fly.

No. Most FBOs (Fixed Based Operators) allow the crew to escort you out to the aircraft and in some cases, you may be able to drive your car right up to the plane to unload your bags.

No. As long as it is not classified as HAZMAT (hazardous materials).
Check here: www.faa.gov

Yes, if you meet the criteria of the State Department 12 classifications.
Check here: www.slate.com
See also: www.federalregister.gov

In general, no. However, most private flights equate to the last minute purchase in first class, using 2-4 people as a guide to costs. Flying privately saves you time, which is money.