The events are in the past, and the writer (who is the child involved) is looking back on them from a time well after the events. Thus "would remain" is chosen, to indicate that the concerns remained a hunch for a time period now long ended, specifically through the end of the pregnancy when the birth revealed the actual condition.
This form, with &...
"could imagine" is correct: it means that at the time it was possible for you to imagine what she was going through.
"could've imagined" is also technically correct: it means that at the time it was possible for you to imagine what she was going through, but it also specifies that you did not imagine what she was going through. While this ...
The use of "could" in place of "can"in these sorts of constructions generally implies something that might happen, but has not not happened yet. Use of "can" tends to imply something that will or probably will happen.
In (1) "could is grammatical, but implies a greater doubt than "can" does. "The most we can ...
I can't think of any context where I would think [some idea that seems to me likely to be true] isn't equivalent to and interchangeable with I would have thought... (ditto for the contracted I'd versions).
The only slight difference is that because the Perfect form (have thought) is "literally" referencing something "further away" from ...
The verb phrase in this sentence is "may be coming"
English verbs can be formed as "modal verb + infinitive"
He may play tennis.
The infinitive can be a progressive "be playing" or perfect "have played" form
He may be playing tennis.
The meaning of the progressive form is surprising: "He may play tennis" ...
She might have been waiting for us.
Here, perfect "have" is a plain (infinitive) form.
"Have" is the perfect auxiliary and "been" is the progressive auxiliary.
The modal "might" is a tensed form and "waiting" is a lexical verb.
I strongly recommend dropping the term 'helping verb'. It's nonsense
Her grammar is non-standard.
This video will be a little different.
also, at a different point, she says:
The more prepared you are, the more successful your interview
This is also non-standard.
The more prepared you are, the more successful your interview will be.
The more prepared you were, the more successful your interview would be.
EDIT - ...
As well as what James K has said, another way to think about it is that you're taking a simple statement of fact:
They are coming sooner than expected
and using may to talk about the chance this might happen instead:
They may be coming sooner than expected
As James said, may is followed by the infinitive, so are becomes be. The rest of the sentence stays the ...
Note that "gonna" is very informal, and you should use "going to"... If you didn't know that, then you will have better luck searching now.
Now, about sentence 3:
You know what would probably happen?
We can shorten "Do you know" to "You know", or even just "Know". That is probably what this sentence is ...