I've never done any Paypal the way you've described. They give me their e-mail address and I send them money through Paypal or I give them my e-mail address and they send me money through Paypal. I've never done an invoice, ever.
And I don't see how they are going to "hack into your account" by simply knowing your e-mail address?? Please expand on that.
I don't like Paypal, but I've used it quite a bit for selling stuff on Ebay, they basically shove it down your throat, and have never had a problem. I set up a Paypal account over 10 years ago and have had no issues. That doesn't mean I like it, just that I use it.