There is an exercie on the book about how to make invitations. It is for writing skills but I think it's more usual when you speak. Nevertheless, if you do it well when you say it, you can do it when you write it.
If you want to see some typical expressions to invite, go to this
link. Then you can do this listening comprehension
here.
As a curiosity here you have a video about Pollock and how he used to paint; click
here
About grammar, here you are a clear video with an explanation (click
here) and then try to do some exercises to work with questions without auxiliaries:
See you in class!