Can a third party fill out my ESTA application for me?

It could be the case that one of the applications in the group is still processing. You can check the individual applications by searching for the details individually. To do that you would need the passport numbers, dates of birth, full names and nationalities of all the people in your group.

Yes, even if your final destination is not the United States and you’re stopping at an airport in the U.S. for just an hour or two, you will still need to get an ESTA authorisation. You may not even be able to board your flight if you do not have a valid ESTA, as your airline will request this before your departure.

Any foreign nationals wishing to enter the US must first of all obtain some form of visa that provides the relevant permission required from the US border control authorities. Different types of visas are available for different types of reasons for travelling to the US.