Well, some of those points are already set in the main DCU if you look at his comics for the last 2 years. And another was pretty constant too except for sidestories for him, like his role in Leviatan, for a few more years previously.
1. He hasn't been a real villain in the main DCU since New 52 (11 years ago). He has been suspected to be a traitor because of his past several times, and has been antagonistic to Bruce in particular a few times in that time. He has also collaborated with a villain a few times too, but you can say the same for other bats, too. He has been a villain in elseworlds and alternate realities a few times too, but again, you can say the same for the others. His allignment place since the new 52 arrived seems to be an anti-hero who has heroic moments and also neutral, rebellious or uncomfortable stands. Some fans who would like him a bad guy or a bastard who can be a villain may not like it, but as I said, I think it is pretty set at this point. For now. Things can change a lot 5 years in the future. Most Jason fans like him an antihero as far as I know. It's the option that tends to win every poll.
2. No guns in the main DCU and more general audience aimed works. It seems to be a problem in certain markets, and they have decided to change it. I think this started in the second half of his last RHATO run, or at least, we were already commenting that back in the day when we saw it shifting towards no guns. There may be more reasons, but at least that one is almost confirmed. It's not going to be a well received change, because most fans like him with guns. But we can't do much about it. And it's not like Jason didn't use a wide array of weapons before, so, well, there's that.
3. DC has decided that he's close to the core fam, enough to go and help them in certain cases and events, but not close enough to be a regular: he's what I call, a "cousin". He's in a similar spot than Cass but not as close as Steph or Barbara are, and seems to have a rocky relationship with Bruce (and only him), which is to be expected. This has been the regular take for the last 5 years or so for most of the writers that used him. It's a place some fans would like to be closer, and some other, farer. So I guess it's not a bad spot in the range.
4. This one is the one that's less set. But again, you can say the same for the other bats, included Batman. I love diversity in stories, so I can't really complain. Fans are pretty divided here, too. Same as Batman fans with this topic.
There's a lot of smaller things that need to be set, as you have already mentioned. But you can say the same about stablished characters, like Dick or Tim, that have been runing for longer. Right now, I think, the one better defined is Damian.
Also, fans never, ever get to a consensus. There's a part that will always complain about ten different things. I guess this is why they try to find a balanced place every few years, for the shifting readership. And why DC never pleases everyone.
Pretty average fan take on Jason. I think.