Yes, there is specific evidence that we will have bodies after Jesus returns. Part of the gift that we receive because of Jesus' own resurrection is the resurrection of our own bodies.
1 Corinthians 15:42-44a
So will it be with the resurrection of the dead. The body that is sown is perishable, it is raiased imperishable; it is sown in dishonor, it is raised in glory; it is sown in weakness, it is raised in power; it is sown a natural body, it is raised a spiritual body.
In another words, our bodies will be resurrected and will be glorified/spiritualized like Jesus' body was when He rose from the dead.
Re: Animals in Heaven
Well, I think it's more than just symbolic though. The lion lying with the lamb. Why wouldn't there be animals? I mean, there's going to be a new Earth. A NEW Earth. Like this one all over again. I can only assume that there will also be plants, animals and other organisms there as well as they are here.