I've never gotten the 'target' with artillery after moving it. I think you're not supposed to get the 'target' ever when your unit cannot attack, but sometimes with planes it does appear, which is a bug, I think.
But, yes, there are definitely many subtle aspects to this game that might take a little while to figure out. It took me a long time to find some things out, and I have played Pacific General before.
I'll list a few here to hopefully save people some time.
1. Rain and falling snow both make air attacks impossible and drastically reduce visibility of planes. Overcast skies just reduce visibility.
2. Rough surface conditions, such as mud, make it very difficult for trucks to move. Units mounted on trucks will have reduced speeds and all units will burn fuel like crazy in bad weather. Supplying in muddy conditions is less efficient, and attacking through mud is very difficult.
3. Level bombers are very ineffective in destroying enemies, but they are still very useful. All units suppressed by a level bomber attack stay suppressed for the rest of the turn. So if you are about to go for a very hard fight trying to displace that heavily entrenched 10-strength Engineer unit, if you send in a level bomber and it suppresses 3, when your infantry finally attacks, that unit will fight as if it was a strength 7. Many level bombers, like Ju88A and HE177, have naval attack capability and are great for killing and suppressing enemy ships. Having at least 1 level bomber in your core is a good way to make sea battles in shore scenarios go your way, especially since the Allies often have a superior navy. Finally, level bombers destroy some of the unit's ammo when bombing. Coupled with high ground defence ability of later bombers like HE177, it can be a good way or cracking those annoying air defence units. Bomb it with a level until it has no ammo, then move in a swarm of Stukas and blow up the artillery all around, allowing your tanks and infantry to finally move in on other units, including that AD.
4. Bridge Engineers and Pionieres have equipment specifically geared for assaulting heavily fortified positions. They never get caught on a Rugged Defence and so are great units for kicking deeply entrenched units out of their 'happy place'
. Once the unit has been forced to retreat, it's no longer entrenched and can be chased down with other units.