Personally, I find that JJ is often not great at showing the passage of time. For some reason, his time-jumps tend to feel more like regular scene transitions instead.
Right? Rey and Chewie's journey from D'Qar to Ahch-To felt like it was a real-time jump of just a few seconds. Jeez buddy, fade to black or something, huh?
Well they went from Jakku to Takodana in just a short conversation about the Force. How far is that? Then they went to the Rebel base(is that Dqar?)Then they went seemingly instantly to Starkiller Base(which is Illum) in the unknown regions. That's gotta be at least as far as ach-to. How long could it have taken Rey to get there? She had the map.
There are hyperspace routes. Meaning you can't always go in a straight path to a destination. Sometimes you have to follow a route from one place to another to get someplace. We don't see that often, but we did get it in Rebels at least once where they had to jump to an area controlled by the Mining Guild to get to wherever they were going, and that they had to go through Mandaloran Space to avoid Imperial patrols, which would only spot them in real space, because you can't track ships in hyperspace (until you can via new tech, or the Force...because its speculated that Vader was able to track Leia's ship through the Force to Tatooine, just it might have just been the Star Destroyer was just really good at tracking ships based on last heading.)
At least TLJ had JJ's weird time-thing to imply to the knowing viewer that there were probably some time skips that weren't apparent. Rogue One has the entire Rebel fleet launch and arrive at Scarif from a dead stop in the time it takes to search a card-catalog. Never mind the hyperspace travel time, they would've had to get to the point where they'd make the jump in the first place. It probably took longer for the squadron just to get to orbit in ANH.
The maps have Starkiller Base's starting location and Illum at the same place though. That they are using massive numbers of kyber crystals in the First Order's weapons and that Starkiller Base is likely has its weapon powered with kyber like most of the old Sith based weaponry. Having a Jedi planet carved into being a massive weapon for the Empire would be just a Palpatine type thing to do.
It's as confirmed as its going to get. Illum, an ice planet, and galactic source of Kyber crystals in unknown space, is hollowed out by a huge secret imperial project. Starkiller base, an ice planet rich in Kyber crystals sitting at the exact coordinates that Illum once sat(but now conspicuously absent), has been hollowed out and turned into a massive superweapon. A project that probably began under the emperor. Illum is gone.
While it's almost certain that SKB is/was Ilum, it's still not confirmed until they feature it in some story, one way or the other. Which is probably exactly why they haven't specified it explicitly yet because for all they know they might end up wanting to use Ilum for something else somewhere down the line or tell a different story of how SKB came to be. It seems to be the policy of the LFSB to avoid unnecessarily restricting or painting future storytellers into a corner wherever possible. I know fans love to play "fill in the blanks" but down that road lies the constant overlapping retcons that made huge swaths of the EU damn near incomprehensible. It's better this way I think. Anyway, as for the timeline of events, I'm pretty sure both movies only take place over the course of a week or two. That is assuming both Jakku and Ahch-To days are more or less the same as a galactic standard day, since we see several distinct day and night scenes from which we can extrapolate at least a basic timeline. At most I'd say there's a day's gap between Rey leaving D'Qar and the Resistance evacuating, simply because they already know their location is blown and they have no reason to wait around for the First Order to get their shit together after SKB and come after them. The only limiting factors would be how long it took the fleet to come pick them up and how long it would take the throw whatever they could carry into the transports and run. I'm pretty sure you're correct. In TLJ Rey immediately steps towards Luke and hands him the sabre, whereas the last time we saw her she was standing a little further away with her arm extended. I think they way they reused the same music cue from that scene may have given some people a false impression that it was the same scene being replayed. Regardless, I'm certain the two scenes are supposed to take place within a second of each other, depending on how long Rey stood there like that before her arm got tired.
Or maybe... She stood there with her arm out for like 5 minutes, Luke just staring at her, and she began to feel really awkward, turned around and walked all the way back down to the ship, where she stayed for 7 days, then worked up the nerve to make a second attempt, which is seen in the last Jedi. Or maybe... She went up the mountain every morning, held out the saber, Luke just stares, then she goes back down. Finally, after a week, she says to Chewbacca "Seven times I've gone up there, and seven times he just stood there, ****ing staring at me!! Do you have any idea how long it takes to walk up those frickin' steps?!" Chewbacca: "Do you want me to come with you?" Rey: "No. I don't need someone to hold my hand! I can do this!" Chewie: "...have you tried just walking up to him and placing it in his hand?" Rey: "Wow Chewie! That's a great idea. I'll try it first thing in the morning."