Needles

Yes.

As OP states, the affected trophies are due to the Teams being deleted. You can still play online and get the other online trophies.

If you’re starting from scratch, the Platinum is unobtainable because the servers went offline on February 6, 2023.

Nope.

Well, if you win one game with a friend and get the “Networking” trophy, then “Neural Networking” should also pop when you win ten games.

It’s unfortunate what happened to the LBP servers (which is why Project Lighthouse is amazing). But due to the CFW requirement, it’s against the site rules, which you can see here:

Because you need CFW to access the server.

New around here, huh? Project Lighthouse is an awesome project, but it’s also a quick way to get booted from the leaderboards on this site.

Any trophies you have earned on one version auto-pop on the other version as soon as you boot up the game.

Online works fine on PS3, and I believe the PS4 version is now back up and running.

Here is what my city looked like in the end: Notice my condos are boosted by 106% because they are surrounded by level 3 tranquility towers and level 6 solar farms (each of those provides a 5% boost). You can also boost your investment bank or battery this way. As you build up, use cheaper housing to increase your population. You can see the cheaper apartment buildings and condos all over my city. You’ll eventually run out of room and need to use the expensive buildings—and expensive buildings will boost your levels quickly. Make sure you’re logging in to the game regularly to collect your resources.

Yes, leveling up will speed up dramatically when you start buying bigger buildings. Stay focused on making your economy produce as much as possible. You’ll get to a point where you can buy and upgrade the most expensive condos and business tower regularly, and you’ll be gaining levels rapidly at that point. At the very end, you can sell and rebuild your buildings for the final levels - but don’t do that too early or you’ll lose your ability to make money and electricity.

The server shutdown date for Dreadnought is now July 11, 2023:

Server shutdown date extended to July 11, 2023: There is also now a 200% XP/Credits boost.

I believe it is cross-play, but I'm not 100% sure.