Hmmm, those sorts of questions make it seem like the account might have been locked for a potential compromise. Which it might have looked like if your account was suddenly accessed from another country when you moved. Even if you cannot answer all of the questions, try to answer the ones that you can.
How did you lose access - you didn't. Tell them that you simply moved, and that to your knowledge, the account has not been compromised. But you might want to check your match history just to be sure that there are no matches in it that look unfamiliar.
Location of RP purchases - this one should be easy. You most likely bought RP in the city/country you were living in before you moved. If you've bought RP since you moved, you can tell them the new city/country as well.
If you bought any RP using a PayPal account, your PayPal account will actually have a record of the transaction IDs, and you can simply log into PayPal to get them. Obviously, it will also have the email address associated with the account as well.
I've never used PaySafe, so I do not know if they have a permanent account or not. Pre-paid RP cards might be a bit difficult, as most people don't tend to save those cards once they redeem them in the game.
Credit cards are also fairly easy, as you should have the physical card, with the digits and expiration date, and all credit card companies send you some form of receipt after making a purchase (mail, email, text, etc). Riot also sends emails after every purchase of RP to the email address associated with each account confirming the purchase.
But again, you don't have to tell them every single thing you've every bought. They probably just want you to provide enough information that they can verify that you are in fact the actual owner of the account. Just try to tell them as much as you can remember.