Learn English – Write to or write for

It's incorrect to use have in the first sentence, since the subject ("Christmas card") is singular regardless of the adjunctive phrase ("along with the letter").

Along with and together with are interchangeable, and to my ear, neither implies whether they should be in separate envelopes.

Even if there is some indication one way or the other, it's best not to leave specific instructions up to implication. If you have to ask about it, chances are very good that it will go over your sister's head.

But as you addressed all these concerns at the end of the question, I feel I hardly need to interfere:

The new Christmas card and the letter have to be put together into the same envelope before sending them out.

You can use in the OST album or on the OST album.

"in the OST album" has the sense, as you mention, of being part of the group of songs that in total are the album.

"on the OST album" originates from the fact that songs are recorded onto the record platter.

In your example, you should write:

What is the chorus singing during the movie's opening?

I don't think you can naturally use on or in here. BTW, chorus is a mass noun, therefore use is, not are.