I'll start this with one point as I often do with these type of question, it's a home game, please keep that in mind. Don't go ruining the fun for the majority, especially if it's a group of friends. If it's a home game with serious money, and a not just friends then sure enforce strict rules. In your case I'd just friendly let them know it's not fair to do that and in a casino or card club this would be considered collusion.
TDA rules are fairly clear on this. Two rules I can think of come to mind to me here.
67: No Disclosure. One Player to a Hand
Players must protect other players in the tournament at all times. Therefore players, whether in the hand or not, must not:
Discuss contents of live or mucked hands,
Advise or criticize play at any time,
Read a hand that hasn’t been tabled.
One-player-to-a-hand is in effect. Among other things, this rule prohibit showing a hand to or discussing strategy with another player, advisor, or spectator.
69: Ethical Play
Poker is an individual game. Soft play will result in penalties, which may include chip forfeiture and/or disqualification. Chip dumping and other forms of collusion will result in disqualification.
Source - TDA Rules
So with the two above rules let's answer your questions.
- Is it collusion if the other two decide to check it down? -
To reach a verbal agreement I'd argue potentially. It's clearly in breach of the two rules mentioned above, if not collusion, it's absolutely bad etiquette, but it may not be from a point of view of they didn't know better rather than group play. I would view this as soft play and I'd lean on the side of a warning followed by a penalty if they do it again, but may be hard to enforce in a homegame.
- What is the poker talk rule in this situation?
Typically you're not allowed talk when multiple people are in the hand, and you're also not meant to talk about what you have. Heads-up you're allowed talk, but not declare things.
- When the 3rd player is all in, can the other two talk like it is heads up?
No, both rules apply here.
Hope that helps!