With regard to the SS-8, if an employer is really unsure about the classification of a new hire it can file an SS-8 to get an IRS determination. The new hire can also file an SS-8 if he thinks that he should be an employee but the company doesn't, or vice versa. This may cause problems for him with the company because many try to classify their employees as independent comtractors to avoid paying their half of the FICA.
I really don't know how often they are filed by employers. I do know that they aren't filed often enough by employees who have been wrongly classified. As far as the weight they carry, if the IRS determines you are an employee then you are an employee. Period.
Regarding how independent contractors pay their FICA: An independent contractor is considered self-employed and files a Schedule C as you correctly stated. If he has a net income then there is a self-employemnt tax calculated on that net income using Schedule SE. This tax is the social security and medicare tax for self-employed people, who pay the full amount and not just half as do employers. As far as paying it, you can pay it when you do your tax return or you can pay tax in advance on a quarterly basis using Form 1040ES. If self-employment is your whole income then you probably want to pay in quarterlies to avoid penalties. If you have just a small amount of self-employment and the rest is employee income you can usually cover the income and SE tax for your self-employment by just increasing your employee withholdings on your W-4. Either way, paying in tax as you earn your income is important because penalties will be levied if you don't.
Hope this helps you, Bob.
Tax questions are really fun.
Have another one?