What's the deal with "there to be"?

I find that none of my students seem to understand the concept of there to be. However, everybody does seem to know how to use it -- in English, that is. I will now address this matter in a concise manner.

Fact 1: The action there to be DOES exist and is not the same as to be.

Fact 2: There to be is haber, and to be can either be estar or ser.

I will now list the common uses of haber (there to be) to indicate “existence”:

1. hay - there is, there are
2. hubo - there was, there were (used with events)
3. había - there was, there were (used with everything other than events), there used to be
4. habrá - there will be
5. habría - there would be
6. quizás haya - there might be (pres. subj.)
7. aunque hubiera/hubiese - even if there were (imp. subj.)
8. ha habido - there has been, there have been
9. había habido - there had been
10. habrá habido - there will have been
11. habría habido - there would have been
12. quizás haya habido - there might have been (pres. subj.)
13. aunque hubiera/hubiese habido - even if there had been (imp. subj.)

Other important and common uses of there to be:

1. va a haber - there is/are going to be
2. tiene que haber - there has/have been
3. puede haber - there can be
4. debe haber - there must be
5. debería haber - there should be
6. necesita haber - there needs to be

Hope this was helpful.

Hasta pronto,

Juan