1) The captain is flying visual approaches backed up with an ILS and routinely arrives at the marker 100 feet low, flies one dot low all the way down, but has a good touchdown and early turnoff. What would you do?
Sarcastic answer: Die a fiery death due to wake turbulence (disclaimer, I fly the Brasilia).
Non-sarcastic answer: "Glideslope." And like
@BobDDuck said, not making the "stabilized" callout. 1 dot high (or more, for us) is a matter of survival; ducking down that far out serves no useful purpose. If it's a habit, the odds are I'm going to ask "hey, we're low, what's up and why?" at some point during the trip.
Incidentally (and I'm sure you know this too), this is an FAR. If he makes a habit of it, I wouldn't be surprised if FOQA bells start ringing.
(e) Minimum altitudes when operating to an airport in Class D airspace.
(1) Unless required by the applicable distance-from-cloud criteria, each pilot operating a large or turbine-powered airplane must enter the traffic pattern at an altitude of at least 1,500 feet above the elevation of the airport and maintain at least 1,500 feet until further descent is required for a safe landing.
(2) Each pilot operating a large or turbine-powered airplane approaching to land on a runway served by an instrument approach procedure with vertical guidance, if the airplane is so equipped, must:
(i) Operate that airplane at an altitude at or above the glide path between the published final approach fix and the decision altitude (DA), or decision height (DH), as applicable; or
(ii) If compliance with the applicable distance-from-cloud criteria requires glide path interception closer in, operate that airplane at or above the glide path, between the point of interception of glide path and the DA or the DH.
(3) Each pilot operating an airplane approaching to land on a runway served by a visual approach slope indicator must maintain an altitude at or above the glide path until a lower altitude is necessary for a safe landing.
(4) Paragraphs (e)(2) and (e)(3) of this section do not prohibit normal bracketing maneuvers above or below the glide path that are conducted for the purpose of remaining on the glide path.
This rule is there so that you don't buzz the orphanage, elementary school, strip mall etc.
2) Before your first flight you see the captain and lead flight attendant having an argument on the jetbridge and then the captain tells you he's not going to talk to her anymore. What would you do?
This sounds like my first trip on IOE at Brand X, actually. Awkward. As. Something. Awkward.
As the new guy, who was therefore crunchy and tasted delicious with ketchup, I was an awkward bridge between the two of them. It seemed to smooth out a little on days 2 and 3, although very few words were exchanged than "cabin secured" between the front and rear ends of the airplane either.
Now, I would look at both of them and straight up ask both of them if this was going to be something that affected our collective safety. If they can't manage to do "two waters and a trash bag, twenty minutes, nine thousand feet" and "ready for taxi" in a civil tone, then they wouldn't be able to work together in an emergency. Consequently, the safety of the operation is compromised by the personality conflict, and a call to the InFlight or Flight Ops MOD (or Professional Standards, as appropriate) would be warranted to 'encourage' the children to play nice in the sandbox.
Some folks just don't get along with each other, but most can/will cooperate and graduate.
3) A thunderstorm is approaching the end of the runway and the captain is continuing to the same runway. What would you do?
"I'm really uncomfortable with how close that thunderstorm is to the airport. I think we should go and hold over (__) or divert to (__) until it moves off so we don't get our teeth kicked in; what do you think?"
followed by:
"This is unsafe, we should hold over (__) or divert to (__)."
followed by:

4) You ask the FO to help clean the aircraft because we are late but he refuses. What would you do?
Does company culture 'encourage' or the position description require the FO to help clean the aircraft?
On an 18 minute turn, you won't find me in back crossing seat belts and so on; there is simply not enough time in our turn timeline to permit me to do anything that isn't safety-related, and my being in the way of the limited cabin preparation is going to make the situation worse, not better. I try to do it on longer turns every so often, but it can't come at the expense of getting safety-related duties (walkaround inspection, performance, wolfing down dinner, etc.) done.