That is an interesting intake, some thoughts on it:
1. The knife absorbing heat is a good explanation since none of Cole's powers until now even gave a hint of not being heat based, someone mentioned how it could be simply because the place is kinda of a morgue so preserving the bodies with low temperature makes sense.
2. As for affecting Mc making him feel sick seems more of a strech, Michael does that with his powers (as far as i rememeber not just while using his crimsom knife) but is very especific to him, sure Tanos could have made Cole's knife with the same effect but nothing indicates that at least for me so i will just keep my mind open.
3. Evolutions are usually VERY bombastic, i mean Jake's was more internal and subtle but he is a mind based superhuman, with Cole being fire based i would expect something much more flashy. Him trembling doesn't seem enough to be sure its because of evolution.
It could be many things, him remebering the fear he felt during his own time as a lab rat, a hint of emotion after killing people that were just like him, being excited to finally get his new weapon, or even feeling cold inside that freezer, all those seem more reasonable as explanations than an evolution.
In fact i think it would be more appropriate for Cole to evolve during his fight against Mc, even more because Deryl will join and Mc can heal Michael and Alice easily to join too.
4. Mc was unable to feel the apostles during Michael and Tifanny second evolution, until he touched Michael directly just to be expelled right away by Power, i assume he is better now after the paths and his reaction does remind the effects of absorbing the apostles memories so i will hold that thought.
We know Great Ocean from the twins infection, we don't know whatever Cole would connect with, though in terms of link i would say that at the moment the affection Mc feels for the twins is comparable to the hatred he feels for Cole, i say this because to me none would be priority for an inconscious link to form, Mc is all about instinct, he learned to form links to higher powers with Syla so now i wouldn't be surprised if he could do the same by instinct.
5. I agree that the twins affecting Mc normally wouldn't make sense, the only explanation to me is the Strenght Eater trait, Malik was held for a good chunk of time by them, there was a lot in play but given the circunstance i expect a lvl 1 spawn of them to be able to affect a lvl 3 even if just a little.
6. Apostles can be protective of the spawns they think are promising, so Great Ocean being pissed and making his presence know seems reasonable.
7. Cole appearance being the same is also a good reason to doubt an evolution, Shen is also one of the orphans and he changed a lot, though that's not a rule at all.
8. I don't even think it would be a premature evolution for the twins considering the timeframe of others, what i would consider is if the requirements for the special twin evolution were met, Tanos didn't say anything about it specifically but i think he implied they should be alone for the "link" to form, if Great Ocean did in fact decide to make an appearance i would say the chances are good.