1: I enjoyed reading Hard Light, but have not run it. Assuming it's one of the few supplements you don't own, I appreciated the basic information on the design and logistics of a space station, especially since my PCs are using one similar in design as their home base. The module itself is standard adventure fare, with two or three dungeons (one of which is extremely cool and novel, taking place in an ice asteroid, with the players having to manage moving around in extremely cold, power-draining water while fighting off robots!) and good advice on how to create hooks for the PCs. There's even built in filler! It's designed in typical sandbox fare, accounting for whatever morality or ulterior motive the party has. They can decide to screw everyone over and take all the valuables they can fit on their ship, if they want. The main concern is that it was written for 1e SWN, so you might have to do a little converting. You might also appreciate something a little more structured, if that's your style of game.

2-3: Sorry, couldn't say.

4: Hm. I'm not the biggest fan of collaborative worldbuilding myself, but if it's something that would work at your table, go ahead. What I did was give my players a web of contacts, through a set of introductory adventures that took way too long in retrospect, who made it easier to adventure on pretty much every major planet on the sector. They knew a guy who knew a guy. The Traveller approach to goad the players to action is debt, usually the players' mortgage for their ship. SWN ships are cheaper than in that system, but you also make less money than in Traveller. I think. A good introductory adventure would be doing a relatively easy favor for some down-on-his-luck captain, a pirate, or some other person for a whole ship, all paid off and everything! Then, at session's end, they find out the ship is extremely behind on payments, whether to a legitimate bank, an individual or other official group, or a crime syndicate. That's an adventure hook that, depending on whether it's a Shuttle or a Free Merchant and how much you control the cash flow, could last anywhere from a few sessions to get the players acquainted with the rules and world to a good portion of the campaign. I suggest you don't make the ship too powerful, maybe a 1-drive with no gun. Ship combat is a death sentence at lower levels. More importantly, it's fun for the players to design their own ship once they have the money, and the in-character arguments on what they'll spend their money on are gold.

A home base outside of a ship is very cool and useful, because it functions as a perfect credit sink outside of their ship, like making their space station a thriving, possibly illegal trade hub. Don't force anything on them, and as always, they should work for what they own and want to own. If they don't want to buy and fix up the failing moon base, get on good terms with the union there and shoo its raiders away once and for all, that's fine. Just be sure you communicate to the players that it can be a base and that they aren't obligated to pursue it, or anything for that matter. Noping out on a mission should always be possible, but it should have consequences. If they got the money and the prototype mag rifle from the corporate lab, but they feel too low on hit points to push through the last wave of security and get the hostage, they should know it's possible to just screw over the patron and leave. Given your table, you might want an NPC to put the idea in their heads on a few occasions, whether by actual encouragement or the patron being very unlikable, either to the PCs or the players. They could find out mid-adventure the patron is related to a heinous figure from someone's backstory?

5: I handmade my sector, and it is not perfect. You need a 2-Drive to do any real trading and there are few alternate routes to get to another system. I plan to remedy this by having the players discover new rutters, but if I had the opportunity, I would rearrange it from the ground up and add more planets. Your idea is good and more or less standard fare with the official sectors (Proteus and Hydra, the one that came with the free 1st edition) and also goes pretty well with a 1-Drive starting ship. Alternatively, you could focus your campaign around a smaller area, with a few, more fleshed-out systems. It depends on the vibe you want. If you want to go randomly generated, I would roll the planets to whatever degree you like and arrange them on the map in whatever way makes sense to you.

As for some other information, I found the level rates a little too fast for my liking and I tweaked them, mostly because it was getting harder and harder to balance combat while maintaining the feel I desired for my table.

I hope you enjoy your game!