Which exchange has asked you for your paypal password? I don't think any exchange ask you such private things and you should not provide these.
Buying bitcoin nowadays is not easy if you want to stay anonymous because they are requiring lots of documents, ID.
I wouldn't prefer to use paypal to buy bitcoins because they are anti-bitcoin(I consider) but it isn't impossible to buy bitcoin through Paypal.
I didn't say they asked for my PayPal password. I said they might as well have.
Some of these strangers want me to practically give them the keys to my house in order to buy BitCoins.
It doesn't sound very safe to me.