Do I have to pay a fee if a recruiter finds me ...

That depends on the company contracts you signed with him. Here the fee is dangerously high 60% of first salary to be paid 20% a month over 3 months for some companies. Before you sign anything about recruiter looking for your job, read carefully!

Only if you have signed a contract with the agency. Most recruiters get paid by the company that is searching for a qualified worker. Be careful there are a lot of scams out there, so be sure they are a respectful recruiting company before you pay for services.

It depends on a few things like which state you live in and if you sign a contract.  If you are called by a recruiter, feel free to ask who pays the fees.  The vast majority of recruiters are paid by the company who is looking to hire.  Generally you have to engage someone to find you a job and pay them a fee based on a contract and for the most part, I'd stay away from anyone who asks you for money to find a job.  There are better ways.

The  recruiter  is   paid  by  the  employer.

You,  as  an  applicant,  need not  pay any  fees.