I love giant epic space battles, so of course I love Fallen Spire. I've done two 9/9 games with it now.
So..
1) The last shard is always on a core world. I've never tried to save-scum it so I don't know firsthand if it's generated on the fly or not. By that point in the game you shouldn't have a major issue clearing to it.
2) Not sure again
3) Here's the best defensive strategy I've found for FS so far:
3A) Planning phase: Plan out your empire in advance so all your territory is behind a single chokepoint. No spire city should be on your front line because you can't build a 2nd hab / shipyard if there's any AI systems bordering the system the spire city is in. Optimally, your entire empire is behind two chokepoints back-to-back with the spire city in the rear chokepoint where it function as a 2nd line of defense, but this is really only possible on large X-maps.
3B) Expansion phase: Take ALL your territory before starting FS. Research Mk. III shields, Mk. III rail turrets, Mk. III laser turrets, and Mk. III beam cannons while you're expanding. This is the hardest part on 9/9 since you're running up AIP and don't have the FS fleet to help you out, but it makes the exowaves much easier to deal with later.
3C) Prep phase: Build the strongest defense you can muster in your choke(s). A lot of the good stuff is galaxy-capped - things like beam cannons, modular forts, forcefields, gravity turrets, armor boosters/inhibitors, golems, etc. This is why a single choke is best if it's possible (and practical). Fortify all the friendly planets 1 jump back as well to pick off any stragglers and function as a fallback position if your main chokepoint is overrun.
3D) Development phase: Research and build a cap of Mk. III engineers. Start doing FS. All the shards should spawn within your territory (except the last one) and you don't have to do anything except defend your chokepoint while they make their way to your home system. Use your Mk. III engineers to power-build your FS cities - they build can an FS city in less than 20 seconds as long as you have the metal banked in advance and you'll only have to deal with whatever exowave material the AI generates in that brief interval.
3E) Breakout phase: By the time you finish the Galactic Capital and bring your Battleships and Dreadnought online the AI will have built up a substantial defensive force (10K+ on 9/9, from my experience) in the system(s) bordering your chokepoint(s). Use your fancy new spire fleet to clean them out. The best way I've found to do this is to bring along a Mk. IV scout starship for counter-sniper and counter-missle coverage, and then right-click to keep them moving and all stacked up on each other so their shields overlap. None of them will die until the AI brings down the shields of all your destroyers, cruisers, battleships, and the dreadnought. When you see only one or two shields still up go back through the wormhole to friendly territory. Repair, repeat until everything is dead. Fully neuter the system(s) and keep cleaning them out periodically to prevent very large buildups.
3F) Expeditionary phase: During this phase your goals are to hack any fabs and advanced constructors that you want but don't have (Mark V turrets are extremely useful, as I'm sure you already know), establish forward bases, and clear a path to the AI homeworlds. If you're going for a standard victory you need a forward base for each AI, if you're going for the FS victory you only need a forward base on the way to the last shard. The forward base(s) should be exactly 4 jumps from friendly territory, within 4 jumps of the AI homeworld, and a Mk. III (or highest available) military command station, spire city w/ hab center and shipyard (and fully improved hab center / reactors, including the Mk III shield generator) and a full cap of all your turrets. Your Mk. III engineers can hop across neutered hostile territory to build/rebuild it and you can access it with remains rebuilders and colony ships via SC jumpship or assault transport. This is important because when your FS fleet leaves it will be destroyed by exowaves, threat, CPAs, whatever. But when you come back it's easy and quick to rebuild and you'll have a safe place to repair / replenish your fleet for the final push on the AI homeworlds (these are great places to engage the mothership, FS fleet + FS city defense makes quick work of them) or when escorting the shard back.
3G) Endgame phase: Homeworld assaults are straightforward - spawn the mothership, kite it back to somewhere you can kill it easily, take out the really nasty stuff with warheads, jump the FS fleet back in, kill it, do the same thing to the other homeworld and you win. The shard is trickier since you have to escort it a long way through hostile territory while defending your chokepoint against exos without your FS fleet there to help. Unless you load up on cheese (all 4 modular forts + superfortress in the same system, multiple golems, many types of Mk. V turrets, high-level champion + support ships, etc) you'll probably need to leave part of your FS fleet behind to shore up your chokepoint defense. If you've built a forward base like I described in 3F you can break the shard escort into two smaller escorts which makes it a lot easier. I've also found success using cloaker starships to keep the shard itself under cloak and group-moving my spirefleet with the shard so it stays under their shields at all times. If you're going for an FS win the escort is harder than the final 30-minute defense, at least in my experience. A fully defended choke + a full FS fleet is practically invulnerable, even when the AI throws 100 golems at it.
4) I've never seen exactly where the exos come from but I have seen them come from AI space that isn't connected to the homeworld and I've seen them come in when I have a presence in the systems immediately adjacent to the AI homeworlds, so they must be coming from warp gates. Beyond that I'm not sure.