For example, Lor San Tekka could have it, presumably to give to Rey when she is ready
And where would he have gotten it from?
Also Han wasn’t taking Rey to some spaceport, he was taking her to Maz. She is Han’s connection to the Resistance. I don’t remember Han even thinking about any other place to go.
Well where did he get the map fragment? I assume that Luke had given it to him, so it wouldn’t faze me at all if Luke had also given him his old lightsaber. It’s a lot more reasonable than Maz having it.
We are still talking about Anakin’s lightsaber here. Luke didn’t have it, as far as we know. Why would he give up his self made lightsaber from Return of the Jedi?
To your other point: I don’t recall if Maz knew where the Resistance was located. If she knew, why were there agents from both sides among the regulars? It makes me think that Maz had a reputation for being a neutral party. Also, I don’t think Han wanted anything to do with the Resistance before the Hosnian catastrophe. Finn and Rey knew where the Resistance was. They were just there for a ship, they didn’t need Maz’s help.
Just because Maz knows where the Resistance is, doesn’t mean she works for them. She obviously knows Leia and due to her knowledge about the Force, she may have met Luke, so that he can learn some Jedi history from her.
Han doesn’t want to face Leia, he wants someone reliable to bring the droid to the Resistance. this means he isn’t looking for some random passage on a spaceship, he’s looking for a trustworthy pilot and he knows that Maz can find him such a pilot. It’s not a coincidence that Han goes to Maz.