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1. We have a serious crisis coming.
2. He got fired. But he had it coming.
What is the meaning of "have" in the above sentences ?
Are the above constructions with "have" similar to that in "I had him begging for mercy." ?
Comments  
Debpriya De1. We have a serious crisis coming.
2. He got fired. But he had it coming.
What is the meaning of "have" in the above sentences ?
Are the above constructions with "have" similar to that in "I had him begging for mercy." ?
All three are different. "To have" has many uses.

We have a situation here. We possess it. It's ours. It's on our hands. (We have a leak in the roof.)

He had it coming. This is an idiom. He deserved it.

I had her in the palm of my hand. I possessed her, but in a different sense from the first. I controlled her.
I had him begging for mercy means that I controlled him, but it's also similar to "I had him mow the lawn," or "I had him mowing the lawn."

These uses of "to have" are probably codified in a neat way in textbooks: 1;2;3;4;5.
Thanks Avangi,
What about the sentence "I had a few words of Latin spoken at me" ?
Does it fall in one of the categories you mentioned above or does "have" here mean "to experience" ?
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Debpriya De "I had a few words of Latin spoken at me" ?
Does it fall in one of the categories you mentioned above or does "have" here mean "to experience" ?
Context here indicates that you are the "indirect object" of an action.

Your example resembles passive voice.

Someone threw a brick at me.
I had a brick thrown at me.

Someone targeted me.
I was targeted.

"To experience" does not cover it. You can "experience" something without an actor being implied.
But isn't "I had a brick thrown at me." different from "I had him begging for mercy." or "I had him mow the lawn." because we don't control the brick or the person who is throwing the brick at me ?
Debpriya De1. We have a serious crisis coming.
2. He got fired. But he had it coming.
What is the meaning of "have" in the above sentences ?
If I may butt in, ...

to have it coming is 'to deserve it', with the added idea that it was to be expected. This is an idiom, and it must be set aside as a special case unrelated to any other usage of have.

[subject] has/have an X coming is an alternate way of saying that there is an X (which is) coming, and that this fact is of interest to the subject -- involves the subject in some way. Like the there is construction, we expect an indefinite noun phrase to be included.

I have an important package coming in tomorrow's mail.
(There is an important package coming in tomorrow's mail. It is for me.)

Variants:
The travelers have a road block up ahead.
He has a dental appointment coming up soon.
They have a package already on its way from Chicago.
The other day I had water dripping from my kitchen ceiling.
The doctor has a patient coming in for a check-up this afternoon.
Lately we have had a lot of squirrels running around in our garden.

CJ
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Debpriya DeBut isn't "I had a brick thrown at me." different from "I had him begging for mercy." or "I had him mow the lawn." because we don't control the brick or the person who is throwing the brick at me ?
If I may butt in ...

I had him mow the lawn ~ I arranged for him to mow the lawn.
They had him wash the dishes.
I'm going to have them finish the job tomorrow.

I had him begging for mercy ~ He was begging for mercy (as a result of being under my influence, in my power).
The stand-up comedian had them laughing uncontrollably.
Before you could whistle "Dixie", Tom had Huck painting the fence.

I had a brick thrown at me. ~ I experienced this: A brick was thrown at me.

See also -ing

CJ
Debpriya DeBut isn't "I had a brick thrown at me." different from "I had him begging for mercy." or "I had him mow the lawn." because we don't control the brick or the person who is throwing the brick at me ?
Yes, absolutely so.

The remarks in my second post were addressed specifically to the example captioned from your second post.

I had a few words of Latin spoken at me. (similar to) I had a brick thrown at me.
My comments included that these particular sentences resembled passive voice. (I was targeted.)

The other examples you mention were addressed previously.

Best wishes, - A.
Okay, I get it now. Thanks.
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