Just looking for some clarification here. Can a Deathwatch Kill Marine from Rites of Battle become part of a Kill Team and then benefit from the Kill Team's cohesion and squad mode, or is he stuck with the Squad Mode abilities he gets from his special ability?

I would say he can and that one man kill team is his solo mode ability.

I don't think I'd allow a kill-team to be a regular PC in a DW game, and if he was that he didn't get to join squad mode.

Kill-marine is clearly designed to be used in situations where the PC is the only Marine, such as in DH or RT games. They specialise on working on their own, and so shouldn't really be great at working as a team, too.

Odd situation might come up that a group consists of multiple Kill-marines. Each has his own Cohesion, no teamwork necessary. Everybody can play their moody loner ******* and still make use of a few Squad Mode abilities.

Moody loner assholes don't get to gain anything from being in a team, to my mind.

A kill-marine is still a DW marine and thus still able to be in squad mode with his fellows. If he's the squad leader he only has the one pool of cohesion, but could wind up using it on his solo mode abilities. If he's not the leader, he has his own pool in solo mode, but can not access it or use it, when in squad mode.