The time frames "currently" and "at the moment" can refer to a temporary situation, but they can also refer to a situation or action that might continue into the future.
Of the two, I would say that "at the moment" most often refers to a transient or ephemeral action/state, and yet, it most often takes present continuous.
But in some cases (with non-stative verbs) it simply cannot take simple present:
- Where are you going?
- At the moment, I go home (wrong)
- At the moment, I am going home.
"Currently", on the other hand, most often applies to actions or states that are continuing, and might continue indefinitely: :
- Who robbed the bank?
- Currently, we're looking into it.
yet it can reasonably take simple present:
- What inventory valuation method do you use?
- Currently, we use FIFO.
So, all I can say is that your prior notions about simple present vs. present progressive were much too constrained.
By the way, for what it's worth: "currently" extends a litlle into the past, whereas "at the moment" doesn't.
And, as you well know, one can say "I am going to school tomorrow." (But that's a different kettle of fish. Or maybe a horse of a different color. Or, more likely, a fish of a different color—namely, a red herring.)
Your initial examples are not as unambiguous as you think, and that is probably leading to later confusion. The continuous effect is not as baked in as you make it out to be.
"I'm having dinner at 2:00" actually sounds like dinner is scheduled to start at 2:00.
"I was having dinner at 2:00" could it was ongoing in the past at 2:00, or the 'was' could be subjunctive introducing doubt, meaning plans were changed ("I was having dinner at 2:00, but I missed the bus so we ate at 3:00"). Or even just that plans have been cast into doubt (eg "I was going to Toshi Station to pick up some power converters" -L. Skywalker)
"I will be having dinner at 2:00" could be grammatically be either ongoing or a scheduled start.
Your simple tense examples mostly work, although "I have my dinner at 2:00" sounds like it means "I have dinner at 2:00 every day" more normal usage for a specific upcoming event is "I will have dinner at 2:00"
Anyway, the main point is that the 'ongoing nature' isn't as firm a rule as you are looking for. So that's why there's nothing broken about "I'm having dinner at 2:00 tomorrow" with 2:00 being the start time.
Best Answer
As the Original Poster expected some of these are indeed mistakes. For example:
We don't use the present continuous with the verb have unless it is being used to describe an action: I'm having a party tomorrow or I'm having a great time, for example.
The present continuous
The present continuous is normally used when some action (or state) is in progress at a particular point in time, or period of time.
In the most simple cases, this is when the action is taking place now. Of course, now might mean right this second:
Or it might mean this year, this month, this week etc:
This is probably the best explanation for Original Poster's example (1) and the "you are sticking to it" part of (2).
However, the time involved is not always now, it can be something that takes place at the same time as another action that is mentioned:
Here Ed's washing up activity is taking place at the same time as my watching TV activity. This is the reason for the use of the present continuous in (4):
The Original Poster's example (3) is a bit trickier to deal with in one way, and much easier in others. This is because it's impossible to establish exactly why the present continuous is being used, but there are two or three reasons that could easily explain it.
First, however, let's look at the phrase constantly messaging someone. This is an interesting phrase because, as the OP clearly knows, we tend to use the simple rather than the continuous for things that happen always/ usually/ constantly. However, people can do things constantly for a short specific period of time. Constantly does not mean "for ever", but "without stopping". So it might be that you went on a date with someone and they were constantly texting their friends. This would mean just that they were texting without stopping for the period of the date. It doesn't mean that this has always and will always happen, of course.
It turns out that there are at least three reasons why the present continuous might have been used in (3), especially because we do not know what the rest of the sentence was or the context in which it was said.
First, it might be that it's used because the time being considered is now. Second, it might be being used because X happens "when you're constantly messaging someone". In other words it's maybe used to indicate that two actions are taking place simultaneously. And there's a third possibility that we haven't really talked about yet.
There's a very frequent use of the present continuous with the adverb always:
Now the Original Poster would indeed be wondering why on earth we are using the present continuous, which is reserved largely for things happening now, when this kind of sentence says pretty much exactly that this happens all the time. It doesn't really fit with the general theories that we read about in grammar books and so forth. It's normally presented as an exception.
However! There is, I believe a very good reason why this is basically the same kind of use of the present continuous as used in (4). In other words it is used to show that one thing is happening at the same time as another. The theory is not yet published.
Some always-sentences would sound very odd if they used the present continuous:
Example (6) is odd if the meaning is meant to be the same as The corpse of King Boll decays in the ground or The corpse of King Boll is decaying in the ground. This is because we tend to use [am/is/are always x-ing] for punctive acts. That is to say actions which can takes place more than once or can take place many times.
Example (7) is a bit odd if said, for example, by me, Araucaria. The reason for this is that, as you might rightly suppose, I have never met Biden. We tend to use the is always X-ing construction when we have personally experienced or witnessed this thing happening a lot. Example (7) implies something like:
In other words, the construction lends the weight of your (or sometimes someone else's) personal testimony that this thing happens a lot. The reason for the present continuous is to imply that this always happens at the same time that you personally encounter it. That's the theory anyhow. And this could be the reason for the present continuous in (4), where the adverb constantly has a similar meaning to always. It might be paraphrased as:
One may wonder why I have talked a lot about things happening at the same time, or things happening now, but I haven't discussed temporariness. Well, the reason is that I believe that temporariness is a very good reason to consider something as happening now, as opposed to always or usually. However, this doesn't work the other way around. Just because something happens usually or always doesn't mean it isn't happening now! What is important is the way the speaker is thinking about the situation.
Imagine if someone falls off a building. A passer-by rushes up to them and puts their ear to the person's chest. What are we going to shout to the passerby?:
The answer, of course is (8), not (7). It is not that we think their breathing is temporary, but because we are wondering if they are breathing right now.
And, come to think of it, you're breathing right now too! And the earth is spinning on its axis. And the moon is orbiting the Earth. And ...