Did you miss that Han Solo had quite some character growth between A New Hope and The Force Awakens? He went from selfish smuggler (with a soft heart I guess, he helped Chewie) to altruistic rebel who risked his own life for the greater good. For a character like that I don't find it weird at all that he would try to save his own son from the Dark Side even if it meant risking his life. Yes, he was that guy. I honestly find your critique more than a little bizarre. It completely ignores Han's character arc and the irrational things people will do for their children. To me there was no way he wouldn't at least try to help Kylo. And even if he'd taken a blaster with him he wouldn't have shot his own son.
An aging gunslinger probably couldn't do much to defend himself from a sith (by another name, I guess) still in his prime. There aren't really any plausible "precautions" that would have helped him anyway.
Han Solo already knows that one can't outdraw a Sith. He tried that, Vader just bounced the shots off his glove and than took Solo's blaster with the Force.
He should've brought a pocket carbonite freezer unit to quickly immobilize Kylo and carry him away, right?
"Never tell me the odds." Han had been pulling off the ridiculous and the impossible his entire career, so why do you think he wouldn't give it a try when it comes to life of his son and to fulfill the promise he made to Leia? Han's part of the Starkiller mission was over. He had planted his explosives and left Chewie with the detonator. Now it was time to make a last ditch effort to bring his son back from the dark side before he left. You make it sound as if they were in regular contact with each other and Han could just ask his son to eat lunch with him and talk out their issues. The only times Han was ever going to encounter his son is when they were fighting the First Order, and even then it was a rare occurrence that they should meet up on the battlefield and have time to talk. When do you suggest the "right time" would be? Ben was expecting rejection and hatred in order to justify his actions to himself and to confirm his demonization of Han in order to prepare himself for killing him. To have him instead show a father's love, tenderness, and forgiveness probably did more in that one second to fuel Ben's inner emotional struggle than a thousand speeches and appeals could. If Ben was truly being torn between the dark and the light and feeling constant pain, then Han's final act may have just been the thing that might eventually begin to set him on the right path again. He'll still be evil for a while, he might still have to die in the end, but I bet at some point he'll be forced to make a choice between good and evil, and the image of his father caressing his face as he died, showing him love and mercy, will be what makes him do the right thing and perhaps make the ultimate sacrifice himself, just as his father did.
The Solo death scene was good and plausible. It was the exactly the kind of impulsive thing a father would do. It's consistent with Luke rehabilitating his own father despite the bloodshed Vader caused. Luke harbours hope that they can both escape before he realises that his fathers death is imminent. Years later, Hans is prepared to forgive his own son to get him back. These intense scenes bring to life what would otherwise be a fairly formulaic film.
Chewie had no problem blasting Ben right in the stomach. Ben is not as powerful a sith as Darth Vader yet. He couldn't even use the dark side to make him aware that Chewie was watching the whole incident with Han above them. Let also not forget that Rey someone who hasn't yet been trained(Maybe some youngling training) in the force easily beat him.