must be/must have is used to show that we are sure that something is true and we have reasons for our belief.
He looks happy, he must be hearing good news
Note that be requires an adjective or noun to follow it, not a verb, so we use a kind of adjective called an active participle hearing. Together with be, this forms a present continuous.
He looks happy, he must have heard good news
Have must be followed by a past participle or by been and a present participle. In this case, the past participle is added, and have heard makes present perfect simple.
In these examples, we state that the reason for our belief is that he looks happy now, but we would need additional information to decide which example is appropriate. The first would be appropriate is he didn't look happy a minute ago but now somebody is talking to him. The second would be appropriate if nobody is talking to him right now but, for example, he has just come out of the boss's office after his salary review.
We cannot directly build a future for this example, as he does not yet know that he will receive good news and so he probably does not look happy, and so we cannot base our belief on the way he looks.
Here is a different example where we can infer a future event from current information:
The blackbirds are singing: it must be going to rain.
I think you could simplify it down to this:
- 'Want' is desire, and is used to express desire of some type. 'Will' has not lost its relationship to 'want,' as 'will' still has the context of "volition" or more simply, "will" (the two are synonyms). It however is not the same context as "do as what you are willing," in which 'willing' means something like "what you'd be comfortable doing, reasonably." It is not a want.
- 'Shall' is closer to 'will.' It implies a lot of volition, more so than 'will,' which is conditional. It implies duty, just as 'must' does, but if taken in a modern context, 'must' is more informal and applies to a more flexible range of time.
If you need an example of 'will' in the more archaic context, here's one.
Best Answer
By most modern understandings, have to and must imply compulsion, should implies obligation without compulsion, and shall implies firm intention or commitment - or is just used in place of will to lend a certain air to the text or speech.
In contracts, standard documentation and various other specialised usages have their own understandings of the term. If you need to understand them legally, you should speak to a lawyer. I know in some cases shall is a stronger term than must, and in others it is the only acceptable thing because the document is describing what each party is committing to do.
To reflect "internal necessity or inner passion", I would say that you are talking about a compulsion, so "have to" or "must" are both appropriate. They are both (effective) modal verbs, and as such can theoretically be used in any tense, though not all modals exist properly in all tenses; "must" is often replaced with "had to" to express compulsion in the past or with "have to" to express compulsion in the future. They are also both used in front of the have of the perfect tense in order to indicate inference in the past, just to be clear.
You have no choice but to park there, or are under some strong compulsion to do so. This is often used in a hyperbolic manner, to express a strong need or desire to park there (or whatever the verb is), without there being literal compulsion.
This means you had no choice but to park there.
This means that you may not remember that you parked there, but all the evidence suggests that you did park there.
You may not remember that you had parked there some time in the past, but the evidence suggests that you did.
Using them about the future restricts you to have to rather than must, unless you use the futurate (the use of the present tense to talk about the future).
That's the future tense with the obligation/compulsion.
That's the futurate.