I absolutely agree that Aizen encourages as much infighting as possible. It relates very well to their nature as hollows because they'd have to be constantly fighting to survive. It's a very different world from the Vandenreich where nothing but teamwork is encouraged. I think Grimmjow's poor treatment is from a combination of challenging Aizen directly and loosing to Luppi (since I think Aizen would look down heavily on the fact that he lost more than anything). Nnoitra seems to know who his boss is and is respectful for the most part, although he does have a strong independent side. As for him explaining away what happened to Nel, I imagine it would go something like this: "Yeah, I got rid of her, so what of it?!" He probably doesn't care what people think about his actions and I don't think Aizen does either.
I think you're right that the in-fighting is a product of their environment. Those who don't want to fight become fuel for those who have sufficient resolve to keep fighting. If left to his own devices, the strongest will naturally claw his way to the top of the food chain.
Aizen was probably secretly amused that Nnoitra was able to defeat someone several ranks higher. That isn't supposed to happen if the rank structure is as rigid as it appears. #8 would normally be unable to do anything against #7, much less #3. If Nnoitra's powers work like Ichigo's and Zaraki's (to unlock more power as needed for a particular opponent), that would certainly bear for Aizen to watch.
I'm not so sure Nnoitra followed the rules but then again, Aizen doesn't enforce them. I have a fan theory that the reason why Starrk showed up so fast afterward is because Ichigo's fighting Nnoitra was unintentional and Aizen had Starrk on standby to help out if something went wrong. I guess we'll never know if the fight truly was intentional or not.
That sounds quite plausible, although perhaps the damage control should have shown up a bit sooner if the intent was to rescue Ichigo from someone he was unprepared to face. All Starrk did was grab Inoue, thereby forcing Ichigo toward the planned battle with Ulquiorra.
IMO Nnoitra wasn't intended to get anywhere near Ichigo, considering how badly Ichigo was losing. His bankai did absolutely nothing against Nnoitra, he didn't even try his Hollow mask, and then Nnoitra handed him off to Tesra. He really would have died if Zaraki hadn't shown up because he wasn't fighting back. Which I think just goes to show that the ranking system isn't tiered as precisely as fans might like to claim. Why would #6 and #4 be planned battles if it means skipping over #5? Doesn't that mean Nnoitra's power should be above Ulquiorra's?
I would like to hear Aizen's logic in his rankings, why he planned those particular battles for Ichigo, why he didn't step in sooner when Nnoitra was obliterating Ichigo, etc. Although come to think of it, if Ichigo had died at that point, IchiThing probably would have shown up sooner. Wouldn't that change the story?
Of course we didn't see Aizen's reaction to Nnoitra's cover story (assuming he gave one), but seeing as Nnoitra had all his arms I don't believe he was punished. Very interesting.
Of course if that drawing is by Kubo and he has said something about Nnoitra, then I'd be super happy too! Just seeing another official Nnoitra drawing from Kubo would be great! Though I agree with Akhal-teke's first impression that it is most likely fan-made due to the different style. 
