Yakuza Kiwami is a remake/remaster of the very first Yakuza game; Yakuza 0 is a prequel to that game which was made later. If you want to play the games in order based on the events in the story, it should be Yakuza 0 -> Yakuza Kiwami.
Just the same, which is better Yakuza 0 or kiwami?
Kiwami is much better than 0, especially in terms of battle system and boss design. In Kiwami the bosses give a good, fun challenge, whereas in 0 every single fight is a cakewalk, even on Legend.
Though, does majima kill Makoto? By the beginning of the seventh chapter, Majima has managed to secure Makoto a safe-house in the form of a storage shed owned by the manager of Odyssey. Majima confesses that he was sent to kill Makoto, though he still isn't entirely sure why that may be.
Yet, is Goro Majima dead?
Majima survives but is wounded in the altercation. Kurosawa orders local newspapers to report Majima as being dead, so as to demoralize the Tojo Clan and incentivize Kiryu to attack Kurosawa's inter-Omi Alliance rival, Masaru Watase.
Can you free roam after beating Yakuza 0?
After beating the main story you are given an option called adventure mode which is like free roam to finish up all side activities.