The rules vary for each country on whether you need to complete one or not if you are just transitting and when you need to complete them by. But yes you'll need separate forms for each country you are going to visit.

In most cases adults need an individual form of their own even if part of the same family group or travelling party.

Check the US State Department or the individual countries websites for detailed entry and PLF requirements.

You can help speed the process up by being prepared with your hotel details and already having photos of your passports and CDC cards ready to upload into the forms and weblinks to the forms themselves.