If + will here is correct and natural. This is not a first conditional expression (or any conditional). The meaning of "if" here is the same as "whether".

It's quite common. "I wonder if they'll go there tommorow." sounds the most natural. The word "If" implies uncertainty and people are always uncertain of the future.

a polite way of asking someone for something such as information or their opinion, or asking them to do something. I wondered if You could possibly grant me some money? I was wondering whether you would like to come to the park with me? I wonder if you would do me a favor?

Simple answer is that #1 sounds correct and #2 sounds wrong :)