I am actually a PayPal employee and I can personally vouch for the company I work for. PayPal is entirely secure and one of the few websites that can boast the fact of never being hacked since their creation in 1995. Please keep in mind though, PayPal is only as secure as its password, so if you ever compromise your password you do run the risk of issues. However, in the unfortunate event that you do have an unauthorized transaction on your PayPal account, PayPal guarantees 100% recovery of unauthorized payments! PayPal does give you the ability to change your password at any time simply by visiting the "profile" page.
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I hope this helps!