Learn English – If they were Vs If They had been

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.

"Were to" is used instead of "was to" because it's an example of the subjunctive: it's explaining a situation that is either hypothetical (as in the case you mentioned) or imaginary, rather than something that is definite.

I am not sure if the phrase "if I was to" is ever grammatically correct. I don't think it is.

If you remove "to", there are some distinctions between the forms "if I were" and "if I was".

If I were stronger than you, then I would win at arm-wrestling.

This is also an example of the subjunctive, and describes a situation that is not currently true, but either could be, or could not but expresses a wish to be.

If I was stronger than you, then I never took advantage of it.

This is not subjunctive, and it indicates an uncertain past: something that might have happened in the past, or it might not.

What would be the meaning if I only used: "… If Chaudhary jumped they would catch him …"?

That has about the same meaning. I would say either is acceptable usage.

He was to become boss but he retired early.

He retired before people expected him to. If he had not retired, he would have become the boss.

He was to come at 5:00 am but the train arrived late.

He was supposed to be there at 5:00am when the train arrived. But the train did not arrive on time, so he got there sometime after 5:00am.