This is a classic Gainax Ending, i.e. an ending where a lot of things happen which are ambiguous or just plain don't make sense. The trope is named after the studio Gainax, famous for these sorts of endings (see also "Neon Genesis Evangelion" or "Panty & Stocking with Garterbelt"), the same studio which produced Mahoromatic. To put it simply, things happen in the anime, but there's no explanation for exactly what happened.
In the case of Mahoromatic, this is understandable. The second season of the anime ended in 2003, while the manga continued until 2004, so at some point the anime studio was forced to either wait to create another season concluding the anime or else come up with their own ending (they chose the latter). Anime-original endings are not uncommon among manga adaptations.
Anyway, here's everything that I've managed to gather from it:
Suguru is now a bounty hunter on the Saint-Earth colony. He works with a comrade, but that comrade later backstabs Suguru in an attempt to collect the bounty on his head. As he is seriously wounded or dying, he sees Mahoro again. Matthew also makes a vauge related comment related to "leaving something behind" as she leaves the Earth to search for more life, which seems like it may be a reference to Mahoro. It's not clear in what form she has been reborn (human, android, or something else entirely), or if she's just a hallucination. Even if she's alive, Suguru is most definitely seriously injured, and it is not explained whether or how he survives.
If one browses through forums and blogs, there are tons of speculative interpretations of this, and none seem to have any official sources backing them up. The only conclusion I can come to is that the ending is ambiguous, perhaps deliberately so. There do not seem to be canonical answers to any of these questions.
For what it's worth, the manga ending is somewhat easier to understand, but it is quite different from the anime ending in terms of the points you have mentioned. There are some similar details, so it may be that the author had some rough idea what he wanted to do but had not finalized the details at the time of the anime's ending.
Matthew (the leader of Saint) was the original basis for Mahoro and the one who proposed her to Suguru's grandfather originally. 20 years after the events of the main story, Suguru is now a Vesper agent and works tirelessly to defeat their enemies. Matthew meanwhile is leaving Earth to search for new life somewhere else, but decides to give birth to a human girl who is the reborn version of Mahoro. As Mahoro ages she begins to remember about Suguru. After one mission, Suguru returns to his home on the Earth, only to be greeted by the reborn and newly human Mahoro. It's implied that they live happily ever after. In this ending it's clear how Mahoro was reborn, and that Suguru did not die and was not hallucinating.