Language families refer to the provenance of a language, the oldest vocabulary. That doesn't automatically mean it will be easy or hard to learn if you speak another language within or without that family. For instance if you speak Spanish you may find it easier to learn Tagalog than if you speak Malagasy (Madagascar), even though Malagasy and Tagalog are in the same family and Spanish is not.

I doubt it. To anyone other than a paleolinguist, Serbian and Hungarian are approximately equally distant from English. And the Finns don't have trouble learning English.

N = 1 here

I'm Dutch and have a close friend who's Hungarian. His English is as good as mine. The only impression I got is that he needed to actively seek out opportunities to speak English whereas in The Netherlands you're bombarded with opportunities.

I do think it helps a bit though, but it's easily trumped by opportunity itself.

Maybe but for kids that’s not important.