Well, I can only give you my opinion on some things and my experience on others, though there are many more with more or different experiences than I have had. I have many friends in all age ranges, (teens to extreme ancient older than dirt seniors) all eager to show me something they are proud of or upset with, everyday is an education here. That being said:
Ukraine does have a slight problem in this area, but honestly not as bad as the USA. (which I can use for comparison). Can you honestly say that that one place is more tolerant than another? It often varies in real life, and from one neighborhood to another.
Your friend is talking out of his @ss. What is defined as danger to you? And how do you know what your children will like? At their ages, they are extremely adaptable. There are dangers in ANY country for children, there always has been and always will be. At least they aren't being kidnapped and trained to kill people by some political freak, or strapping bombs on them selves eager to die for some nebulous cause.
Your children will be raised in Ukraine. Try not to isolate them from the world by keeping them in a little Euro box. (Skip the International School attitude, that is for people who are here for a short time) Their education will be Ukrainian, not Dutch. The system here is vastly different from what I had when I or my own children grew up with. If they are going to live here, let them live, children are extremely adaptable. Your 8 year old will have to be on the fast track for Ukrainian. Unless she is a complete idiot she will pick up the language very fast, the other two will pick it up faster. I came from an extreme multicultural country, my boys learned Spanish from their friends and English in school, the youngest hung around with some Vietnamese and in less than a year was able to converse with them in their tongue.
Point Four: Beats me! No experience in that area here in Ukraine.
I have two kids here, not my own, but currently they are 10 and 17. The parents and Doctors dote over them like they are a precious natural resource, which they are. Health care even in my city is pretty good, but huge problems need to be addressed in Kiev. Health care insurance is not very expensive. I have a heart condition, but I am not worried about it, much ...
This is Ukraine, not Russia. Looks like the kids will learn both. Who are you to chose for them how they speak? You are only their parent, their friends will speak what they speak and so will your kids. Again don't keep them in a little box. At their ages it will come to them very quickly, English is also taught in school. You can't just decide on your own which language they need to learn, they will learn what the need to get along here. I think Ukrainian is the best bet, Russian will follow along at the same time. SERIOUSLY do not underestimate the brain of a kid dropped into a new environment, I can not stress this enough. YOU will have more problem(s) learning than they will. Guaranteed, unless you already speak Russian or Ukrainian.
Is this a problem with Ukrainian youth? I am sure it is a problem in many places. So you plan on dropping the 1,3 and 8 year olds at a party attended by wayward teens? NO, you are just gonna worry about that LATER when they are older, hell, things change. When I was a kid (1960's) in San Francisco Bay Area is was free love-sex, drugs and rock-in-roll, it' isn't that way today. You clearly missed the 70's in Berlin also, and Berlin without the Wall, is not what it used to be by a long shot.
So for the couple people at home, if they haven't been here they can not speak about it with any intelligence at all, because nothing they say has any Ukrainian experience behind it right? A friend hears from someone about a party, big deal. I hear lonely Australian men like to have sex with sheep, is that true? More than likely NOT. I hear in Ukraine all girls want leave Ukraine and are nothing but gold digging prostitutes. Is that true? No, absolutely not. I hear in Brazil women go topless on the beach is that true? Well, yes, yes they do, (seen it first hand) though SOME should not. Hearsay is mostly all crap.
Ukraine like most places is what you make of it. Your kids will do okay, the problem is you are moving them here and they will no longer be like the children of their original country, what could you possibly expect? They will have Ukrainian mindsets and values, thanks to you.
Most Expats on this forum who live here 24/7 365 days a year have little real problems. As long as you are here full time you will learn how to adapt faster and stop relying on getting things done back in the home country. Problems will be solved faster, you will make friends you see everyday, and trust me things will get easier. Ukraine is much different than we are all used to, this is a society with a different mind set, maybe someday that will change, but then every country/culture has it's own mind set ... you are about to enter the Twlight Zone.
Just my opinions.