If it's not directed towards anybody, does a question still require a "?" ?

If it's a question, it needs a question mark. A question not directed to anyone is a rhetorical question, but it's still a question.

That's three sentences separated with commas. Two of those sentences are not questions, but the third one is. I'd write it like this:

Immediately, I knew something was wrong: it was only six thirty in the morning. Who would be calling so early?

...or like this:

Immediately, I knew something was wrong. It was only six thirty in the morning. Who would be calling so early?

April is right. The comma splices were very distracting.

"Who would call at six thirty in the morning?"
"Who calls at six thirty in the morning?"

...are alternatives. They're not past tense either, but nor should they be in my opinion. But if you did want to use past tense, maybe:

"Who would have been calling at six thirty in the morning?"

jennifer75 said:

How about this:

Immediately, I knew something was wrong. Who would be calling at six thirty in the morning?

And....does that read in past tense? It kinda sounds present.

Click to expand...

Much better. You've eliminated the comma splices and cleaned up unnecessary wordiness.

If "be calling" is bothering you, you could make it "Who would call ..."

But it isn't present tense; I think it's that modal auxiliary thing.

FennelGiraffe said:

But it isn't present tense; I think it's that modal auxiliary thing.

Click to expand...

Yes, it is. Okay, here I go:

First:

April Holland said:

But if you did want to use past tense, maybe:

"Who would have been calling at six thirty in the morning?"

Click to expand...

That would work, but whether to call it "past tense" or not, is another question. The original would work, too.

Here's the thing:

Modal auxiliaries often come in present tense and past tense forms (present tense/past tense):

will/would, shall/should, can/could, may/might

Two modal auxiliaries have no past form:

must/-, need/- (need rarely occurs in the positive as a modal auxiliary; it's almost always in the negative: "you needn't go there"...)

These auxiliaries, since they do not have a past form, either occur unchanged in the past (rare, possibly obsolete; I'm not sure), or - which is more common - are replaced by quasi-modal auxiliaries:

must/have to; need/need to ("you needn't go there," = "You don't need to go there").

They're quasi-modal auxiliaries because they take auxiliaries themselves and thus behave more like main verbs than auxiliaries (e.g. "you don't [=auxiliary] have to [quasi-modal auxiliary]...")

So far, so good. But there are complications. The past tense forms of the modal auxiliaries don't always have past meanings.

Will/would is a good example:

"Will" can have the meaning of "insist on":

He will play the guitar, until his fingers bleed. It's no good telling him to take break.

​

This meaning is easy to transfer into the past tense:

He would play the guitar, until his fingers bled. It was no good telling him to take a break.
​

See? "Will" turns into "would", with the only difference being tense.

But once you get past this, it becomes tricky. The past tense form of "will" not only marks tense; it also can imply a theoretic situation:

He will not kick a kitten. (This implies an actual refusal. It has somehow come up that he should kick kitten, and he refuses to.)
​

He would not kick a kitten. (This is theoretic. Nobody asked him to. But if somebody asked him to, he would refuse.)
​

Now the theoretic meaning has a version, where the theoretic kicking takes place in the past:

He would not have kicked a kitten. (This is a theoretic past event.)
​

Now, if you transfer the theoretic meaning (either "theoretical present event" or "theoretical past event") into a past tense narrative you run into a problem: the "would" is already the "past form" of "will".

The difference between "who would be calling" and "who would have been calling" in your context is one of general vs. specific. If you use the "who whould have been calling", you're making it specific to that day. If you said "who would be calling" you're taking a broader view. There's very little difference between the two versions, in effect. You can use what sounds better to you.

I probably didn't explain this very well. This is one of the most discussed issues in tense; experts don't agree on how to interpret this. The thing is, though, however hard it is to analyse, it's quite easy to use. People do it all the time. You did it, too. This is one of those issues where thinking too much about it probably hurts you more than helps you.

Simple "would" is okay. I do think most would agree to that.

If it's in dialogue, or close narration, I would use a question mark any time you want to indicate rising intonation at the end of a sentence. Whether it is a question or not.