Help on being self-employed/1099? I don't understand.?

Hi. I am a 20 year old full time college student still living at home. I recently got hired as a web designer in the beginning of August for a car stereo company. The store manager told me that I will be a self-employed employee, and told me to make sure I take money out of my paychecks. I make around $200 a week... show more Hi. I am a 20 year old full time college student still living at home. I recently got hired as a web designer in the beginning of August for a car stereo company. The store manager told me that I will be a self-employed employee, and told me to make sure I take money out of my paychecks. I make around $200 a week ($10 per hour), sometimes the hours vary slightly, and I get paid in cash. When I got hired, I never filled out paper work, I just entered my social security #, name, and address into the computer. When they pay me, I do not receive anything that shows/verifies my hours. I am just really confused. None of this got explained to me really. How much should I put away each week? And should I ask for monthly verification of my hours so when I get my 1099 I will know they didn't mess up/screw me? What does the quarterly thing mean? Will they send me the paperwork or do I have to send something in to the IRS? Does this all sound sketchy?

Thanks for anyone's help.
Update: I am not sure if I can ask for checks. The one time I did get a check it bounced! So freaking weird. He caught it early and paid me in cash/& the late fee though. Which if this happens again, I am quitting.
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