Learn English – “Have this been” or “Had this been” provided

I don't think your idea can exist.

In your sentence...

I can have had been reading a book if I could send a letter back in time to tell myself.

... the conditional if and past-tense makes your opening can illogical.

Instead,

I could have been reading a book if I could have sent a letter back in time to tell myself to read it.

-or-

I could have read a book if I could have sent a letter back in time to tell myself to read it.

-or-

I could be reading a book if I could have sent a letter back in time to tell myself to be reading it.

If you're writing fiction, and the idea you're trying to communicate is that you could be doing something else right now if you could change the timeline, I would say it like this:

If I can send this letter back in time to myself, then I can have read the book before it's too late.

When you try to say "I can have had been" you're creating a time paradox. Consider the following:

I can be reading if I can send myself a letter back in time to tell me to be reading.

If the above is true, why aren't you reading? And if you were reading, you couldn't be sending yourself a letter to tell yourself to read, so you wouldn't be reading.

So, like I said, I don't think the idea (as you've expressed it) is able to exist, the grammatical problem merely uncovers the time paradox.

The first two are grammatical. In the first, married is the past tense of marry, and is here used intransitively.

In the second, they were married is a passive construction, and married is the past participle of marry. Although it is passive, the agent is not mentioned, but we can reasonably assume that they were married by a priest, or by a government official.

The third is ungrammatical because the past perfect construction describes a past event that precedes another. It is clear in this case that the wedding took place only after they had been engaged, and not before.