In written English you would use the verb to be (unless you are writing what someone is saying), but in spoken English you can shorten the sentences as Peachey has explained. You are also more likely to say "there's so much happening, rather than "there is so much happening".

It's a condensed form, or note form, which we use to be brief. In regular English (ie. 99% of the time), we use a full sentence. There's nothing wrong with adapting those short phrases to full sentences.

Those are not complete sentences. "to be" is required to make them complete: Ann is calling. So much is happening.