havent watched the seed/freedom yet but what i can tell from all the promo and word-of-mouth, the pilots of minerva joined up with kira and the rest. so this extra ending which never showed in seed/destiny titled Tomorrow where Shinn finally find some closure to the horrors and traumas when Orb got invaded the first time bridged who they end up on the same side.
as for lacus being president, i can speculate that due to her altruistic nature and campaign throughout the series finally make people of the plant to trust and elect her as their leader after the warmonger Zala and delusional Durandal.
It's added scene from the special edition and remaster of gundam seed, you can find those on the official gundam yt channel (gundam info) from time to time ( they usually publish one of the gundam anime it's entirety for a couple month )
(also publication of seed/destiny was cut a couple month ago so they should come back at some point further this year I think)
At the end you have that memorial scene, then the scene where you see Kira as joined zaft as a white mantle and is escorting the eternal, Lacus becomes Plant president for some time
(without going into spoilers for Freedom, Lacus isn't president of the plants anymore in it and yes minerva's people joined her and kira into their new peace protecting thingy called compass ( it's told in the trailers and small videos published about seed freedom) )
Though seed freedom suffer from much 'things have happened but we won't explain them' which is a bit obnoxious..