Learn English – “I had a dinner” vs. “I was having a dinner”

The simple answer to your question is that you don't use a past construction to talk about the future. We talk about the future using will, going to, present continuous, or present simple.

The only guess I can make for what your friend heard is that she heard reported speech, and the 'is coming' became 'was coming' because of the back-shifting of the verb when we report. Could she have heard something like "The forecast said no rain was coming till tomorrow"?

You don't normally use Present Perfect with stative verbs (have, be, like, seem, prefer, understand, doubt, know, etc.) Here's a longer list - in general, they apply to states that last for some time.

In some contexts, such as "How long have you had/been having these symptoms?", there's no real difference. Arguably, been having calls more attention to the fact that you're still having the symptoms, but I doubt many people would consciously either make or hear that distinction.

A "rule of thumb" for to have is: when it means to experience, you might want to use Present Perfect; when it means to own, you almost certainly don't.

Here's an example for to be using the "slightly unusual" Present Perfect in a construction which is perfectly valid, and is probably the most succinct way of expressing the intended meaning...

By now the new cook will have been being introduced to her duties for several weeks.