Is it invalid to say that some event might have "happened" for some observers in the universe, but not for others? According to relativity, there is no simultaneous "now" throughout the universe. I assume a question about whether an event has happened in a sense might be invalid as the block universe is a static object. Imagine the question "what happens in Andromeda now?", is that an invalid question? What about "what happens in New York now?"? Or, what about "what happened at the big bang?"?
I am trying to wrap my head around which statements can be made regarding an arbitrary event happening or having happened.
Is it invalid to say that some event might have "happened" for some observers in the universe, but not for others?
 A: In Special Relativity, every event “happens” for every observer. But different observers will assign different coordinates to them and they might disagree on whether one event is before, after, or simultaneous with another event.
In General Relativity, “horizons” can prevent events from being seen by all observers.
A: Your question talks about what seem to me to be two different notions: "happened" and "happened now."
What relativists usually talk about is whether event A is in the past light cone of event B. If event B is on the world-line of an observer, and A is inside B's past light cone, then A is an event that, at least in principle, could have been known to the observer at B.
Relativists don't normally talk about "now." It's not a meaningful concept in general relativity.
A: None of your questions are invalid. While it's true that there is no absolute definition for the concept of "now", that does not make it an invalid concept.
When you ask "What happens in Andromeda now?", most people would assume you are asking what events are occurring in Andromeda at a time that would be described within your own reference frame as simultaneous to the current moment. The obvious answer to the question is "I don't know because the information of those events hasn't had time to reach me yet", but the question still has some validity and can eventually be answered retroactively.
That said, since Andromeda "now" is space-like separated from here and "now", there are observers in other frames of reference that would (eventually) disagree with us about what is happening now in Andromeda. For some observers, it's entirely possible that the events we would recognize as having happened "now" they would say were yet to have occurred. So, in a way, you could say that some events haven't yet happened for some observers in the universe. Or rather, you could say that there are some events that we would say happened before now and some observers would say happened after now.
It should be noted that if two events are time-like separated, then that means there exists an absolute chronological ordering between them. Essentially, what that last statement boils down to is that if we are currently aware of an event that happened before "now", then there does not exist any observer anywhere that would claim it happened after what we call "now". The only events for which there could be a disagreement about whether or not they happened by the time we reached this exact moment of "now" are those that we are too far away from to know about yet.
Of course, just because there is a disagreement sometimes about chronological ordering, it doesn't mean the notion of asking what is happening "now" is invalid. It's just a bit ambiguous and partially unhelpful.
As for asking about what happened at the big bang: The big bang is a moment of time, which means if you point to a position in space that we'd recognize as being at a later point in time, everyone else would agree that it's a later point in time. Additionally, since the big bang represents a moment of time defined as the time when the universe held a certain property, all observers would say that what happened at the big bang was that the universe held that certain property. It's really kinda trivial.
A: The question “what was the weather like in London at the time the Elizabeth Tower clock struck 12:00 on 22.12.2019” is well-posed. Some observers will be unable to answer it due to spacelike separation from the event, but all observers that will know the answer will agree on the same answer.
The question of whether the aforementioned event preceded or succeeded a certain event in Andromeda can have one of three answers: either the spacetime interval between the two was spacelike, meaning observers can disagree which one came first, and neither of two events could have influenced the other; or one of two was first and all observers agree which.
So a certain event will have happened for some observers (who will agree on its outcome) and it won’t have happened for others. As for “now”, in SR you can only talk about “here and now”. To establish some semblance of simultaneity in distant locations, you have to start from a common point in spacetime (e. g. construct two clocks in the same location and then move them to different galaxies), then you can define meaningful calendars. You’ll be able to ask questions like “if our clock, instead of going to our galaxy, went to their galaxy, what would happen in its immediate surroundings at the time it would display such and such time?”, but the answer to that would depend on the exact path through spacetime that it would take to that galaxy. If you fix a certain spacetime path for both clocks, you can say that “now” is when their clock has the same reading as ours, but other pairs of clocks delivered by other means will have differing concepts of “now”.
The best you can do is to say “this event could have causally influenced that event”, i. e. the spacetime interval is timelike. Whenever that is the case, all observers agree on that.
A: 
Is it invalid to say that some event might have "happened" for some observers in the universe, but not for others?

According to both classical mechanics and relativity, if a physical event happens for one observer, it will certainly happen for other observers too. However, in classical mechanics, the occurrence of the event is simultaneous from the standpoint of all observers because of the absoluteness of time (simultaneity ), whereas in relativity, the event may occur in different space-time coordinates from the viewpoint of different observers because simultaneity is not absolute. 
It is also emphasized by R.A. Martins [1] that, in any theory which includes a one-to-one space-time coordinate transformation, if an event such as collision, explosion, etc., happens in one coordinate system, it will necessarily happen in another one too. 

[1] R. A. Martins, “Length paradox in relativity,” American Journal of Physics 46 (6) 677 (1978).
