I loved that they used Leia’s Theme - made my eyes water. I’ve been sort of dreaded the end of the Saga and Leia. Read somewhere that Ep. IX was originally going to be Leia-centric - makes me sad that story is not going to get told. 
+1! That Leia theme gives you all the feels. And as much as some people criticize a certain scene in TLJ, when that music kicked in it left me a mess in the theater. I couldn't help but think about Carrie Fisher in that moment, and that music did it to me again here in this trailer.
I'm with you there about wanting to see how this story might have played out had Carrie still been with us and was able to see it through to the end. But I'm also glad that the filmmakers were sensitive and respectful enough to not try to force something on us with a completely artificial performance. Tarkin was one thing in Rogue One. Leia is at the emotional center of the Star Wars Saga, and a level of authenticity to the performance is important.
As for Palpatine laughing? Where does that go? There seem to be a number of paths that are open based on plot points from other moments in the saga.
-Does it tie in to Palpatine's conversation with Anakin at the opera in ROTS? Has he found the way to cheat death? He even said it in ROTS as he spoke to Anakin following his turn against Mace Windu - "To cheat death is a power only one has achieved. But if we work together I know we can discover the secret". Is this real or an allusion to the Force spirit phenomenon?
-What about the world between worlds as seen in Star Wars Rebels? Ezra use the portals to rescue Ahsoka from her confrontation with Darth Vader. And he encountered Palpatine trying to use the portals as well.
-In ROTJ we see Palpatine fall and the explosion, but that's all. Could Palpatine have escaped in some way using the Force? The one point where that might not work from a story standpoint is why would he then abandon his Empire? But we can also keep in mind his line from ROTS to the Shocktroopers after Yoda fell but they were unable to locate the Jedi Master. Palpatine said "Then he isn't dead".
-A holocron. They can be imbued with the spirits and thoughts of the Force users that create them. Could a Sith holocron made by Palpatine be among Kylo Ren's most valued artifacts?