About to extend non O visa for my dependents (based on my WP). When I checked with immigration about the requirred documents the officer told me that there is no need to do the visa for my 15 months old kid, but if I want to be perfectly legal, I may apply. Sounds strange...we will be taveling a lot abroad, wouldn't the lack of a visa of my kid raise some eyebrows at the airport immigration? Any thoughts?

Children are not charged for overstay.

Yes it would and overstay stamps would be placed in passport but no fee involved. In your case, with frequent travel, probably best to get the non immigrant O and extension and re-entry permit for returns as visa or visa exempt is required for entry and visa exempt runs risk of airline blocking travel without onward tickets.