Hi, welcome to the forums.
There's a couple different mechanics you could be referencing when you talk about the path the AI takes and where the attack comes from, so let me give you a couple answers here.
The question might be "say a wave takes out my planet, where will it go next?" If that happens, the ships that overran your planet will revert to being threat. They could immediately attack a neighboring planet if they think they can take it, or they might congregate on nearby AI planets until they spot a weakness or opportunity to capitalize on. They use the same mechanics that AI ships use if you enter a planet, tick everything off, and then leave without killing them. You can see the total # of ships in the galaxy released as threat in the top status bar. It's worth actively clearing threat ships out if the # gets too big.
On the other hand, you might be referring to exowaves. Exowaves are targeted strikes spawned at the AI homeworlds (usually; fallen spire exowaves can spawn from any warp gate) that have a specific target (some structure) and travel straight towards it. These happen if you have a superweapon (broken golems, spirecraft, etc) enabled. I believe the path highlighted on the galaxy map is the path the ai would take? Someone will let me know if I'm wrong. However, depending on the source of the exowave, they can have targets other than your home command station.
As for your other questions:
You don't mass upgrade turrets, that's not how the game works. If you unlock higher mark turrets, you can then build those in addition to your existing turrets. All marks coexist, basically.
As for the galaxy overlay thing, a lot of those screens in AARs are photoshopped (alternatively, I need to learn a few things). But the game does give you some options. Bottom-middle of the screen, where it says Displaying:, you can click on that box and then the game will show whatever you select. Some of the most useful display options are ARS, fabs, threat, science collected.
Also, if you look at the left bar, however, you'll see P0 through P9, right? You can click on those and then assign them to planets, and that will show up on your map. So you can mark all planets that you want to capture P9, and all planets that you want to neuter and clear P0, or whatever.
As for your last question: it really depends. You're gonna have to decide whether it's worth taking the planet(s) between you and what you want to capture. The decision typically revolves around factors like how often you're going to be sending ships along the path (will it be a chokepoint? a staging base? or do you not care if you hold it once you get the ARS or whatever you captured it for? things like that), how many planets you'd have to take to cut a path, are those planets in the middle themselves worthwhile and defendable, etc.
If, in the end, you decide not to slash and burn, you have a couple options. You can just right-click to get there and fight your way through. As you do so, you can destroy guardposts along the way to neuter the AI planets and keep the path relatively free of reinforcements. You could also use transports (assault transports have cloaking & fast movement, they're really good). As you play more you'll get better at doing surgical strikes far outside your territory.
