Will my fire pit rust?

Yes it will. There are no industrial paints that resist direct flame contact.
You may see by the end of the season shadows of rust.

What can I do to maintain it?

At the end of the season use a steel brush in and out, and apply another coat of Thurmalox 270.

What can I do to extend life of the fire pit?

Do not try to cover it under a plastic tarp as it would trap moisture.
Half a sheet of plywood on top is plenty sufficient.
Keep the drain hole at the bottom clear.

How long will the mesh last?

Customer feedback shows that even after 5-6 year the inner mesh is still doing its job.
If the mesh needed to be replaced, undo the self tapping screw replace the damaged one with a new one, install a new self tapping screw.