Yah, I think it was spot welded. As suggested above, rivets or sheet metal screws will do the trick. Rivets a bit more clean if you have the gun and rivets and since they are usually aluminum, you won't have to worry about rust.
Yah, I agree with Larry. Use smallest possible. I use the 1/8" on a lot of my rehabs but my needs are more robust than your situation calls for so the 3/32 rivets would probably be best. Make sure you use the correct size drill bit for making the holes. You can usually get by with one that is the same size as the rivet if you wiggle it a bit after drilling the hole. But typically, the process calls for a bit just very slightly larger than the rivet size.. I use a 1/8 bit for 1/8 rivets and works for me just fine.
Oh, I would just verify that those rivets are made of aluminum. I see no mention of that on the package while the boast "All Steel Construction". If they are plain steel, they will rust and create a mess.
You could, but they will rust pretty quickly on the back side. Are you sure they are steel rivets. They are not very common. If they are, I would spring the few extra bucks for a small pack of aluminum ones. Probably won't cost much more than some spray paint.
I would say they are aluminum. If they were steel you would need a stronger rivet tool.
I 'm pretty sure the rivets on weber kettles and WSM's are steel because they do rust, but nothing to worry about.
Here are the ones I have. All aluminum, shank and all. Either Menards or Homedepot.....can't remember which. But I think you can get them most any hardware store.