Here's how I would have done the Han Solo death scene. In this version, I'm not going with the 'Han is trying to convert the bad guy' storyline, which I found to be a little ridiculous. Whether Han is Ren's father or not in this, Han has at least accepted that Ren is evil and will always be evil. Ok, here we go.
They're on the ice planet/death star III. They've just rescued Rey and are running back to their ship (which if you remember is right on the edge of that cliff). Kylo Ren is in pursuit. They get to the Falcon but in true Falcon fashion, it won't start. Han goes to check something and realizes what's wrong, but it will take a few minutes to fix. Chewie and Rey start working on it.
Cut to Finn, who is in the cockpit freaking out. He yells back asking how long this is going to take. "Few minutes", they yell back. As Finn looks back forward, Kylo Ren is right outside the cockpit. Ren starts to force choke Finn through the glass. Then we hear it
"HEY!"
Kylo Ren looks over and sees Han Solo, standing on the edge of the cliff outside the ship, holding a tiny container over the cliff (Han has snuck out of the ship to get them away from the rest of the group)
"Leave them alone, or I drop the map!"
Ren steps back off the cockpit window, "Give it to me"
Han puts it in his shirt pocket. "Come and get it"
Ren moves towards Han. Han reveals that he's taken Luke's lightsaber. He fires it up, but it's clear he has no idea what he's doing.
Ren fires up his lightsaber and begins to attack Han. Han can only block, badly. After a few blocks he gets thrown down by the force of Ren's attack against his block, facing away from Ren.
Ren walks confidently up to Han and raises his saber for the kill stroke. Han turns slightly and fires his blaster that he had been unholstering while pretending to be down for the count.
The shot hits Ren in the shoulder and he's thrown back, yelling in pain. Han rises again with Luke's saber and they go at it again, with similar results. Han is completely outmatched against Ren and after 4-5 valiant but desperate blocks, Ren stabs Han through his chest.
Han falls to the ground, face down. Ren turns him over, and rummages through his vest pocket, opening the tiny container. Ren looks confused and angry
"...what is this?!?!?"
"My bar tab", Han grunts as he laughs and fights to breathe. "Ask me what this is...", he says pointing to his left hand. He's holding something in his fist.
Ren opens his fist, panics, and begins to run.
BOOOM.
Chewie, now finished with the repair, runs half way down the ramp just in time to see what happened. He lets loose a fierce howl of pain and sadness
The smoke clears. Ren is injured but alive. Han is dead.
Cut to the Falcon, Rey is firing up the Falcon for departure.
Ren stands up and turns, just in time to see the Falcon flying up and off the planet.