I'm sorry if this was something I missed but since I have never played the game I am not sure what all the units do like are some of them supposed to not deal damage?
Hi TwinLeaf Clover !
It's not the simplest of games for sure, though surely worth it once you've got the knack.
Here's a short written explanation of how to play: https://lambdanaut.com/posts/2020-06-25-How-To-Play-Picowars.html
The only unit that can't attack is the APC. It's for carrying infantry and mechs far so they can strategically capture distant bases.
Some units(the Artillery and Rockets) are ranged. They can only attack at a range. That is explained in the guide.
Good luck and have fun!