A lot of it comes down to how the speaker/writer wants to describe the verb in question.
In general we use Present Simple when we're describing the action as a state.
Present Continuous is used for several reasons, and here are the most common ones:
- The verb is ongoing and not completed.
I'm having lunch. Call me in ten minutes.
- The verb is expressed as something temporary or at least new and not assumed permanent.
I'm following a new diet.
I'm living up the street.
- The verb recurs and its duration includes the present.
She's calling me every day now.
(This emphasizes the repetition; if we wanted to describe it as a state, we'd just use "She calls me every day.")
- We're emphasizing the activity or energy in the verb:
Every Saturday night when I go out I'm drinking like crazy.
Every Sunday morning when I get up my head is hurting.
Now to your example sentences:
That's why my hand shakes.
This sounds odd because in this context my hand doesn't usually shake. You can still use it but it has a subtly 'literary' affectation about it. (This is based on my experienced. Maybe in another country's English this is more common.)
...now he apologizes every other minute.
This sounds fine, as it's expressed as a new state of things. It would also be natural to say the following, to emphasize the temporary and repetitive nature:
...now he's apologizing every other minute.
Why do you laugh?
This is another example of 'literary' affectation and is idiomatic. You may say:
Why do you laugh?
Why do you smile?
These aren't normal state verbs (as in "Why do you wonder?", "What do you see?"), and they're more often used in the Present Continuous than in the Present Simple.
In Example D I would prefer the Present Continuous to emphasize the temporary and repetitive nature of the verb:
Why are you calling her so much?
This is also pretty common:
Why do you keep calling her?
Note that above keep is used as a state verb and calling is now a present participle.
(By the way, in English we call people and don't call to people. This is a really common mistake for non-native speakers.)
In the final example, it's more natural to say:
...the members aren't discussing it anymore.
This is because we're thinking only about a temporary context of the conference, which will last a finite time. So for the remainder of the conference, they aren't discussing it anymore.
Another good way to express it is:
...the members won't be discussing it anymore (for the remainder of the conference).
Lastly, note that we can bend common practice for effect. I can say both sentences in each pair below:
I love this music.
I'm loving this music.
Now we're leaving.
Now we leave.
It breathes!
It's breathing!
These can be subtle and up to the speaker's or writer's creative choice. You can find more descriptions about these exceptions online if you want to learn more about them.
Best Answer
Senses, emotional and mental states, desires, opinions, and measurements are not usually perceived by native English speakers as processes and thus aren't usually couched in the continuous/progressive form.
These examples are highly non-idiomatic and would require an elaborately described scenario to make sense as normal English utterances.
This does not mean "I am in the process of being relieved," but rather "I am in a state of relief." It certainly does not mean I am eternally in a state of relief. I ate. I feel relieved. The relief is tied temporally to having eaten.