During which time or stage of development can diet influence gene function and impact healthy food habits of a child

Generally the Formative stage, being before the age of 5 years old.

Some questions that could appear on a physical activity profile may be...

1 - How often do you exercise per week?
2 - How many hours do you spend doing Physical Activities?
3 - Do you have an exercise routine? and if so, what are they? 
4 - What got you interested into physical activity? 

Those might be some.

I hope I was able to help out :D