I can't speak to how things are set up elsewhere, in New Civilisations you can indeed recruit a great many famous heroes from the shows, books, games etc. We just added many Cardassian heroes in a recent update. You receive a pop-up event notifying you when they are available to recruit - they are classified as Promising Leaders, they start less powerful than Renowned or Legendary Leaders but have much potential! Archer is bit of a special case because he is in the pool ready to be recruited from the very start (so are a few of his colleagues) - be sure to grab him before the pool refreshes though!

You can build a type of ship called Exploration Cruisers if you want to simulate the Enterprise fantasy by sending one special ship out to explore the galaxy. This allows you to have a Galaxy, Constitution, NX etc. class ship named whatever you prefer go out and explore. It requires an Ascension Perk though. Our view is that the Enterprise doesn't itself as a ship have any magic powers that make it a mighty "flagship", rather it is the crew who are special, and you can recruit a great many of these characters as mentioned above.

To form the Federation you need to run the Agenda as one of the founding nations - it's not automatic.

Scrambles pretty much summed it up there. Our view is to avoid railroading players. This is a game, and removing player agency takes away from that.

The conceit is that you are the one running Starfleet (or the equivalent) for your empire. If you want a ship named Enterprise, then commission one by building it and giving it that name.

If you want Janeway to patrol the Neutral Zone from a Cheyenne class ship instead of an Intrepid, then do that. If you want her exploring in an Intrepid named Voyager, then do that too. The tools already exist within the game without the game presuming you want that.

Thank you both for answering me! So to understand, if I am missing the leaders showing up in time there is no way I can recover them, right? It is possible that it's for this reason that, in year 2170, I don't see Archer at all? Also as Exploration ship, when you say exploring systems, it means surveying them? Or just exploring, like unlocking them, but I still need a science ship to complete the survey?

I really like the concept of this mod, like having the freedom to do what you want to do, so not following any rail track, this is also one of the reason why I do prefer NC over NH. Thank you!!

Survey, yeah! Exploration Cruisers are essentially big science ships.

Archer is available from Day 1, so yeah, by 2170 he won't be showing anymore.

To be honest, I did restart an another campaign and Archer is not available anymore at the year 2156. Perhaps do you want to reconsider extending his availability for a couple of years more? I think a reasonable time to have Archer disappearing from the list would be 2165 or 2170. Even the ship research is so pretty random that sometimes you can see the NX class available around 2155, and on another walkthrough I've reached the year 2180 and still no NX class research showing up on the list (meanwhile I had the frankil refit, minuteman, gamge, poseidon, etc.). Any insights on how the ship research works? How can we prioritise certain type of ships rather then others?

He'll disappear from the list when it refreshes, so about five years. I dunno, that seems like plenty of time for people to hire him if they wanted him?

Ship research works pretty much the same as any other research in the game, with the exception that you can choose to ships that are obsolete appear in the list. Stellaris uses randomly drawn options, so randomness will inherently be a part of it. The point of the system is for players to make decisions based on what's presented to them at the time, not to try and plan out every single item of research in any specific order.

On a related note, is Michael Burnham in the list of scripted Promising leaders? I saw a lot of DISCO people in my Federation game but didn't spot her.

No, not at the moment. Perhaps to celebrate S5 of Discovery.