Punishments are separate for different offenses - if your 2 week ban was for chat, then only another chat offense would even risk a permanent ban. AFK, leaving, feeding, etc. would all be independent from this punishment.
To prevent another punishment, you simply must follow the Summoner's Code. You seem to be able to grasp what you did wrong, so I'll just point out some highlights from it:
Supporting your team means building them up, not tearing them down. Encourage them after a mistake - don't try to micromanage/analyze it. People don't change in one game, especially when they've moved on and are trying to win but you keep bringing it up.
Driving Constructive Feedback means providing feedback - tactfully. The right time, the right place, the right manner. Spam pinging someone question mark when they fail to ping MIA? Not the right time, not the right manner. Nicely reminding them once to please notify team if laner missing? Right time, right place, right manner. This goes for feedback for pings, communication, gameplay, itemization, etc. Constructive feedback is not criticism. It is feedback.
Facilitating Civil Discussion is simply not saying anything if you don't have anything nice/useful to say. If you want to be sassy towards someone (ex: "Why?" or "wtf") just don't do it. There's absolutely no reason for it. It's not civil at all.
Enjoying yourself but not at others' expense means that you won't berate or flame someone just to make you feel better. It doesn't matter how you feel if you're making someone else feel like crap.
Showing humility in victory and grace in defeat means you behave the same regardless of if you win or lose. You aren't gloating, and you aren't blaming. You aren't flaming and you aren't taunting. You're being honorable regardless of the situation, and treating your teammates as if the game is going on regardless.
Being resolute is kinda an archaic one that's been updated (the entire Summoner's Code has been updated from the website I linked, but it's still the most in depth one on the web). This one basically means you don't give up. While it's not prohibited to call a surrender vote, or even to state your reasoning, pressuring your team to surrender, constantly telling them the game's over, things like that are not okay.
I didn't cover every facet of the Code but hopefully that helps.