Solid Foundation
I don't think you need a solid foundation in obedience in order to be successful at agility, because obedience is something you continue to work on or add on.
Natural
Kids are natural dog trainers, it shouldn't be a problem with kids, but with a baby, they do not have developed sense of balance or motor skills yet. Give it some time. :)
Yep
Yep, that's a Julius Harness. Still a dangerous world out there, for the driver and other motorists. Strap your dog in, but please be careful when you drive. Avoid texting while driving. :)