A very thoughtful and hard question indeed; it pushed me to research a bit on the subject Continuous Conditional.
Your first example is a past perfect continuous sentence. In general, it is used to indicate an action was happening before another action happened. However, it can also be used to indicate past unreal condition. For example:
If I had been talking to him when he said that, I would have punched him in the face.
But fortunately, he was not talking to him when he said that and that's how he missed my punch.
So according to this theory, your first sentence which is
If I had been with you, I might be taking care.
is absolutely meaningful and grammatical.
Now, there is a vital fact when using these type of constructs as described by data.grammarbook.com,
When talking about something that didn’t happen in the past, many English speakers use the conditional perfect (if I would have done) when they should be using the past perfect (if I had done).
For example, you find out that your brother saw a movie yesterday. You would have liked to see it too, but you hadn’t known he was going. To express this, you can use an if – then clause. The correct way to say this is with the past perfect in the “if” clause, and the conditional perfect in the “then” clause:
Correct: If I had known that you were going to the movies, [then] I would have gone too.
The conditional perfect can only go in the “then” clause — it is grammatically incorrect to use the conditional perfect in the “if” clause:
Incorrect: If I would have known that you were going to the movies, I would have gone too.
More examples:
Correct: If I had gotten paid, we could have traveled together.
Incorrect: If I would have gotten paid, we could have traveled together.
Correct: If you had asked me, I could have helped you.
Incorrect: If you would have asked me, I could have helped you.
The same mistake occurs with the verb “wish.” You can’t use the conditional perfect when wishing something had happened; you again need the past perfect.
Correct: I wish I had known.
Incorrect: I wish I would have known.
Correct: I wish you had told me.
Incorrect: I wish you would have told me.
Correct: We wish they had been honest.
Incorrect: We wish they would have been honest.
So this theory, in a nutshell, says you can't use "would" part with the "if" clause, rather it should be used in the result clause. So, according to this theory, your second sentence stands incorrect.
I don't know why OP says "the sentences are not interrogative". Obviously they are, regardless of whether the question mark is present or not.
1: How could you know if you have cancer?
2: How can you know if you have cancer?
OP has taken his two examples from titles of articles, in which context there's no possibility of them having different meanings. They'll both be followed by text answering the "title" question by setting out possible ways to self-diagnose that you have cancer.
In other contexts it would be possible to distinguish different implications. For example, interpreting could as the past tense of can in #1 leads to...
1a: How was it possible for you to know you have cancer? (perhaps implying disbelief or surprise)
...or one could see could there as equivalent to would, indicating an "irrealis" context. Using could/would like that "distances" the speaker from his enquiry ("I don't actually think I've got cancer - but if I did, how could/would I find out for sure?")
Best Answer
The primary difference between the two is in the implication of the result.
"You should" carries the connotation that if you do as suggested, the outcome will be favorable; it puts the focus of the statement on a positive consequence. You could say that it is an encouragement to engage in good behavior.
"You'd better", on the other hand, carries the connotation that if you fail to do as suggested, the outcome will be unfavorable; it puts the focus on the negative consequence. You could say that it is a warning about engaging in bad behavior.
If the phrases were extended, you would almost always see something along the lines of
vs.