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When to use coming Monday and when to use next Monday? Can they be used in a single long sentence like "On coming Monday, I'll do this, and next Monday I'll do that"?
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The PoetWhen to use 'this coming Monday' and when to use 'next Monday'?
They are essentially interchangeable.
The PoetCan they be used in a single long sentence like "On this coming Monday, I'll do this, and next Monday I'll do that"?
No, that is just confusing (even when corrected by me): both actions occur on the same day.

Next Monday, I'll do this and that.
This coming Monday, I'll do this and that.
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Or you could say "On Monday/this Monday/next Monday I'll do this" (all three refer to the same day) and "on the following Monday (a week later) I'll do something else."
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Comments  
I'm not sure about your 2nd answer. I meant on Monday which is coming in 3 days, I'll do x, and on Monday which is 10 days ahead, I'll do y. If my sentence is incorrect, can you give me a few examples of how to correct it?
The Poet I meant on Monday which is coming in 3 days, I'll do x, and on Monday which is 10 days ahead, I'll do y
No; 'this coming Monday' and 'next Monday' are the same day; I have already told you that. You will have to use something like 'the Monday after next' if you wish to differentiate.
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 khoff's reply was promoted to an answer.
NEXT bears reference to an earlier stated time. E. g. 'I may pay a visit this Monday or the next.' If there is no such reference point, THE PRESENT is the default reference point, wherefore COMING MONDAY is apter than NEXT MONDAY. Is my understanding right?

Let's assume you say these things on Thursday, October 22nd.

I'll call you on Monday.

I'll call you next Monday.

I'll call you this coming Monday.

They all mean that I'll make the phone call on Monday, October 26th

Clive

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CliveThey all mean that I'll make the phone call on Monday, October 26th

Right, from the vantage point of Thursday. I tried to answer this earlier, but I discovered that it's not as simple as it seems and chickened out. If it is Sunday, October 25th, "next Monday" might mean November 2nd, "Monday" or "tomorrow" being sufficient for tomorrow.

Yes, it's a tricky topic.

I think it's best for learner to tackle it step by step, not all at once.

Clive