Bag Accessories

My backpack has some badges on it. They were nice badges, but sadly, most of them were ruined by the rain.

So I've gotten the idea to replace them with patches because if I remove the badges, there will be holes that will bother me even if they're so small no one can see them, and I also don't want my bag to look too boring.

The main problem I have right now is that I can't tell what material it's made from. It does seem synthetic, but there's more than one type of synthetic fabric, right? And I couldn't find any tags or anything to say what it's made from. So I wouldn't want to risk ironing these patches on (although the iron's buried somewhere in a cupboard anyway).

So what are my other options? I wouldn't be good at sewing them on, especially with how stiff the bag's fabric is. So I would have to use glue. But which kind? I need a fabric glue that's strong and won't come off in the rain. Where will I find that?