Can you get problems down there from being fingered?

No. But you can get infected if he has sharp nails and dirty fingers.

can you cite your sources on the whole "sex before 16 that you can get problems in the vaginal area and maybe get cervical cancer" thing? Because I've been googling it for a few minutes and I can't really find any support for that. I don't think your age alone plays much role in whether you get cervical cancer, but I suppose I could be wrong.

edit: ah, I did find something that said your risk for contracting the virus from someone else is increased if you have sex at a young age. Make sure your partner is clean.

And I'm pretty sure getting fingered won't cause cervical cancer. Just make sure their hands are clean and well trimmed.

There's a chance you can get an infection if the hands are dirty if your vaginal tissue is scratched

If his hands are dirty you can get an infection especially if he accidentally breaks your skin.