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.
Of course it isn't safe but for those exchanges that might asked for paypal password then you could say to them do you want my debit card details lol.
I have read that now some exchanges besides verification ID they also ask to hold the ID and take a pic or video as well which I consider absurd.
I would suggest you to try and find someone who lives near you, your city or in your country and deal with him physically.