To the first bold, that makes 3 the best, as you REALLY see their dynamic and how they get along/run things in the orphanage; it's probably the best game for that, along with 1.
To the second bold, I hear you loud and clear; I don't (and never have) disliked the guy, but I'm sick to death of Majima; he grates on you as a character and is beyond-overbearing.
To the third bold, we just had a (small) discussion on this in the Yakuza thread; the series only glorifies organized crime if you take it as face value.
Nagoshi and the writers (sans Seishu, who I think DID try to glorify in the first 2 games) have created plots that show all this glamour and money on the surface, but the undertones and... can't think of the word right now, but meaning will do, the undertones and meaning of what you see and play, is that the like of a Yakuza is absolutely *not* all glamour and is full of nothing but heartache, sadness and loss; a lot of 3 Saejima's story in 4, the entirety of 5 and 6 and now 7, convey just how awful the lives of each character are, even if they find happiness here and there.
Kiryu, specifically, notes aloud numerous times in 3, 5 and 6, that he doesn't want this life as it brings him and the people he loves, nothing but sadness. But he's so deeply-ingrained in the Yakuza lifestyle, he can't get out.
When a game makes you feel empathy, you know it's written superbly
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6 has 0 of weird twists; it builds it up and reveals BEFORE the actual ending.
The issue people had with the end of 6 was who you actually fight (which isn't a big deal in the slightest), as opposed to how things went down.