I'm currently living in the US on an F-2 visa. I know that I'm not allowed to be employed nor to get paychecks nor to have a business even if it's online.

My question is, what about having an online shop that is based in my home country and run everything from there except the shipping (all payments go to my local non-US bank)? So, no received payments get into my US bank account. I will have my buyers send payments to my international Paypal account and then withdraw to a local bank in my country.

Is this OK?

That's doable but be careful with taxes. If you need to report taxes in US, apply for ITIN.