The warnings are a good thing and all, but I'm not entirely sure where Gazans are supposed to go.
As to the bolded, there is some question on that point, sadly:
http://www.nytimes.com/2014/07/17/world/middleeast/gaza-strip-beach-explosion-kills-children.html
(warning on the above link - the NYT had a reporter in the immediate area of the attack, and there's a very graphic picture of one of the dead children)
I don't think Israel, or the IDF, by and large, targets children intentionally. I
do think they have their own militant factions which aren't above it. Whether or not that's what happened here, it's certainly a common perception taking root around the world regarding the incident.