The PayPal one is a rather common phishing exercise. Easiest way to tell if it’s genuine or not is where it says “Dear ...”. Genuine PayPal emails always use the full name you registered with them, not just “Customer” or any other generic title. I see a lot of them at work (where we don’t even use PayPal).
Another way to tell is if you just mouse over the link they provide the real address will come up on the status bar in the bottom left corner of your browser. If it says anything except paypal.com you know it’s a scam.
Affirmative… my actual Paypal email address is on a different account and they address me by name. That one was pretty simple for me, but for some people I am certain this is the reason we end up reading about people giving away their private/personal information and sending money to “the bad guys”.
On another note, some of them are going to greater lengths these days. My brother actually received a signed, letter in the mail from a lawyer in Singapore asking if he wanted to stand in for some guy with the same last name who supposedly died and left 9 mill in the bank. Of course the lawyer was quite willing to split the money with my brother if he wanted to. While I’ve seen these scams via email for years this is the first time I’ve actually seen them send a letter that must have cost them something to print and mail out.