Answering assuming I'm NOT "the DM" on the dive.
* What would you do if you reached your agreed upon turnaround pressure and your buddy or the DM pushed on with the dive (rather than turning around)?
I would first ask, using hand signals, if they intend to push the dive beyond the plan. If they do not understand the hand signals (which should not be the case, since we discussed them on the surface), I will use my wet notes to eliminate confusion. If they confirm the intent to push the dive, confirm the length of time and evaluate gas. If gas is insufficient (or I don't know how to evaluate that) or communication just isn't working, thumb the dive. Otherwise, confirm the push and carry on.
* What would you do if the DM leading your boat dive went into a cave or other overhead environment?
If they had briefed me on it at the surface and it was within the limits of my training, I would have planned gas accordingly and I would have no issue (pending a gas check prior to entering to ensure that I still had the necessary reserves). If it was NOT briefed and/or was NOT within the limits of my training, I would thumb the dive or form a new plan with my teammate.
* What would you do if your buddy inexplicably descended deeper (100+ fsw) than the two of you had discussed during pre-dive planning?
Depending on the depth they had hit, my training, and my available gas, I would likely make one attempt to stop them, perhaps somewhat forcefully if I felt they were impaired in some way. If I stop them, remaining gas and an evaluation of their mental state will dictate whether to thumb the dive or not. In no case will I violate the limits of my training such that I would put myself in danger. If that would be required, I will attempt to signal the DM and/or make an expedited ascent to find trained help.
** This is a big part of why I think sites where the hard bottom limits maximum depth are the best choice for relatively inexperienced divers, or dives with new buddies. At a minimum, it (generally) significantly increases the amount of time you would have to notice and correct this type of issue before too much depth is achieved.
* What would you do if your buddy wanted to go diving but you weren't comfortable with the dive conditions (high surf, current, low vis, rough seas, etc.)?
I would politely decline, and suggest breakfast instead - my treat. Discretion is often the better part of valor, as they say. If they persist I let them know that they are more than welcome to dive with somebody else, but I may or may not be waiting on the beach in my drysuit for a rescue if something goes wrong.
* What would you do if your buddy gave you "the thumb" on the dive but everything seemed like it was OK?
Given that I always discuss command hand signals with new or otherwise unfamiliar buddies, there is no question of what to do. I repeat the hand signal back to them, and begin an ascent. If they have an issue with that, they are more than welcome to discuss it on the surface before the next dive. In the case of relatively shallow shore diving, the next dive could begin about 1 minute after hitting the surface if all is otherwise well.