Can I buy used cell phones and sell them at my store?

Inside City limits or in Cook County? More detail needed.

There are also IP issues: what trademarks will you use? how? what warranty will you make? what representations? will you unlock the phones? etc. See an IP attorney, as well as a business attorney.

Assuming you have acquired legal and lawful title to the devices, that you have acquired the power to transfer licenses to any software installed on or used by the devices from the rightful owner or licensor of such software, and that you are disclosing to prospective buyers that the devices are used and being sold in an as-is condition without any warranty from the manufacturer, then I would say yes. However, getting answers to ALL of those questions may not be easy.