"Is a platformer still the best idea for this?"
Yes. A thousand times yes! Side-view platformer is hands down the best perspective for indies due to the ease of art asset creation.
Top view is also easy, but for having anything like jumping it becomes much more difficult for the player to resolve what's going on, since heights in that perspective are tricky to convey.
"If you want the background to just repeat and play on a mobile phone or tablet, would 2k by 2k save much space?"
If you're worried about space, use tiles. Don't use a huge background image.
"Check out my first hand drawn and scanned tank. I have not colorized the wheels yet.
I will scale this tank down more, this is just start. What do you think?"
It looks good so far! The wheels are the trickiest part, though. Make sure you use some photo references to get the details and colors right.