Last year at 5 DS1 went to some drop off partys and some where I stayed. The drop off ones were mothers group friends and I have known them and trusted them for 5 years so was not an issue at all. I am not comfortable dropping him off for a party where I do not know the parents well.

As for the movies I would ask ad say you are taking your DD and she would like a friend to come alone would blah child like to come and just say you are welcome to come along as well. We have done movies a few holidays in a row and I have always asked a friend with kids and kids have a ball. They have always paid own way.