Well, this are some of the ideas. Note that if I refer to something already appeared in the EU it's just to reuse the element, like sometimes GL did. The EU doesn't exist, here.
First of all:
THE POLITICAL SITUATION OF THE GALAXY
I don't see the galaxy happily reestablished as a cohesive Republic, but divided in many systems and sectors.
If you think to *real* history, we can compare the SW galaxy to ancient Rome. A Republic that grows up to include almost all known world/galaxy and in which there are growing corruption and crisis. A civil war and then the Consul/Chancellor use the situation to became Emperor.
When Rome falls, despite the efforts to keep the nation united, the former empire is divided in many little states. Formally, the legacy of the empire is transferred to the Holy Roman Empire, but the new state is just a portion of the old one, and it's not a direct heir, if not in the name.
The same for the SW galaxy: I see the galaxy divided in small "nation" of independent systems and sectors. The fall of the Empire caused a lack of centralized control. The rebels, that we have to realistic imagine fighting the last resistance of imperial army, after ROTJ are even without the Senate, dismissed by Palpatine some years before, dealings with imperial warlords, and with the needs of thousands of systems oppressed by 25 years of dictatorship and war.
They're able to take control of the core worlds but not the other systems. So, in the period of the sequels we have:
The core worlds, a democratic union of planets that largely collects the legacy of the old Republic and that is formally governed by "the Queen of her People" title which Leia is invested now (maybe it was firstly Mon Mothma)
The hutt's sector, governed by the hutts.
The mandalorian sector (because Boba is alive, right?)
Ossus, or whatever we want to call it, where Luke established the new jedi temple. Because in a galaxy divided the temple in coruscant could have been seen as stand for the core worlds, but luke wants the jedi to be seen as a peace force ro *all* the galaxy, despite political division.
Then a lot of sectors, systems and planets (naboo sector, with its queen, bespin ruled by the administrator in cloud city, etc)
and, at the edge of the galaxy, the unknown regions. Never been part of the republic nor the empire.
The relationships between the system can be different, maybe are usually quite good, but with some suspect towards the core worlds that represents the centralized government the galaxy doesn't want anymore.
The jedi are usually well received as they not stand for anyone and have members from any race or system.
JEDI AND MARRIAGE
Ok, Lucas here messed up *a lot*, and the EU got the situation worst.
From what we know from the prequels Jedi can't marry and have children. Fine. So the same fate will be for Luke (no Mara Jade or Ben Skywalker)
But what about Leia? By retconning her as Luke sister in ROTJ, GL made her be both the future bride of Han and future apprentice of Luke. So? She can't be either of them. So the most logical solution is made her marry Han, have children, become ruler of the core worlds as the "Queen of her people" and avoid just the Jedi fact that could prevent her from any of this roles.
As not Jedi she's able to continue the skywalker's bloodline and have to children that will be young adult at the time of the sequels (do we want to call them Jaina and Jacen and use those good names)
I see Jaina (daughter of the actual sister o Luke) in the role it should have been of "luke's sister" in the sequels guidelines. And so, made her the main character of the sequel trilogy (as Luke was in the OT).
And Jacen should not became a Jedi, both to keep them rare (the Jedi are extraordinaries, not ordinary people. what special about them if they're all Jedi?) and to allow him to continue the skywalker bloodline (yes, he his named "solo" but it's still grandson of Anakin.
JEDI, FORCE, PROPHECIES
How many? If the sequels are going to happen 30-40 years after ROTJ, considering that Luke is been trained in about 5 years (not true, I know, just some weeks in 4 years period, but it's just to make it simple) and assuming he has started training someone just after ROTJ, we will have 2 Jedi 5 years after ROTJ. And if both of them are going to immediately train someone else, we will have 4 Jedi in 10 years. Continuing, 16 in 15 years, 32 in 20, 64 in 25, 128 in 30, 256 in 35, 512 in 40 and go on.
So, it doesn't matter how many they are. Just that in the time of the sequels we can have dozens or hundreds of Jedi.
Then, what's the force? what's the prophecy? The prophecy "of the one who will bring balance to the force" what's the meaning? really? The old Jedi interpreted it as the one who will destroy the sith. but the story of SW shows us something really different. Shows us the one that through the dark destroyed the light and trough the light destroyed the dark. And by doing he reflected in his own life what happened to the galaxy and to the force. The Republic became empire, the jedi are destroyed, Anakin became Vader. The Empire and the sith are destroyed, Vader is once more Anakin. And the force too reflect this: in AOTC the jedi cannot see clearly, as palpatine in ROTJ.
So?
The Force was created by GL with strong oriental influences and many of its principle came from buddhism of taoism. Both the stories of Anakin and of the galaxy are a circling tao: in TPM we have the jedi at their climax, with no enemies, the yang. then the sith are discovered. The black spot. in AOTC and ROTS we see the light/yang becoming weak, the dark/yin becoming strong and Anakin slowly approach the dark side. To the end of ROTS the light is no more, the dark won both Anakin and the galaxy. But Luke is born. The white spot. through the OT we see the rebellion gaining strength over the empire, and luke becoming strong in the light. up to the victory of the light. Anakin was the one brought balance to the Force by making the Tao do a full circle. This is not clearly explained in the movies. My idea is Luke discovering about the prophecy and interpreting its meaning (and through him, let the audience understand)
But the continuing circle of the Tao implied that now that we are are at the climax of the light, a new black spot have to rise. the force/tao as to do another cycle. and this is what has to happened in the sequels.
Stop for now. I'll arrange more material for tomorrow. I hope to have interested someone! :)