You probably are being paranoid about the cc pictures. You already have to type in your cc #, expiration date, and cvv code on the back anyway. I can't imagine of any way this increases your chances of identity theft or anything like that.
Hm I don't recall any buying limits when I started using the app. That might be a new policy. When I started using it, I bought like $1k in gc's over the course of a couple days (I buy discounted eBay gc's, use those to buy discounted gc's to other stores from eBay, and sell them for profit). The actual developer of the app called me to confirm that it was in fact me making all of those purchases (they're a small startup).
I've had a great experience with the app. They sell eBay and Target gc's at better discounts than what I can find elsewhere. And they're delivered instantly, which brings me to my next point.
The way they've implemented gift card delivery (it's instant) allows for a completely different use case than buying gc's from traditional gc reseller websites. If you buy from sites like Cardpool and ABC Gift cards, you might have to wait for it to come in the mail (they do sell digital ones that can be emailed). Then once you get it, you have to keep track of it, making sure to bring it to the store. Then you have to keep track of whether you used up the gc in full or not.
But GiftMe has instant delivery. Meaning you can just go to a store, ring up your stuff at the checkout line, and then tell the GiftMe app how much you want to spend at the store. It will do its best to search for a combination of gift cards that add up to close to how much you're spending, but not more. This way you always end up using your gift cards in full.
No waiting for cards in the mail. No forgetting to bring your gc. No tracking of whether you used your gc's or not.
If the request for a photo of your cc still bothers you, then so be it. But I can't conceive of a way that sending a photo exposes you to extra security risks that typing in your cc #, expiration date, and cvv code does not.
And as for the drivers license thing, you could just start out slowly with purchases.