First of all, yikes.

Those people in the OP had it REAL rough, and they have my sympathies. Don't know how much those were affected by "luck", though. Especially suicides. Those are caused by complex emotional and social problems, not luck.
Anyway, yes, I believe in luck, and that it works differently for everyone.
In my case, I'm insanely lucky. Most of the time, things just work out for me. Not phenomenally, but usually pretty well, especially when I'm in a tight spot. It's kind of insane. 0_o
Another friend tends to have bad luck a lot of the time and keeps getting into bad situations, but his luck functions as a sort of "damage control". Accidentally crack his skull while home alone as a kid? For some reason, his grandparents happened to be be taking a walk nearby even though they almost never do, and they decide to drop in unannounced literally a minute after he cracks his skull. That saved his life. Another time he got hit by a car that decided to run a red light, while on a bike, with NO helmet. Survived with a concussion and bruises, doctors told him that by all rights he should have died. The guy might get into bad situations, but he keeps somehow pulling through when it really matters.
Meanwhile I have another friend who's a really decent guy, but holy shit his luck is awful. Accidentally steps on a nail because his boss forgot to have the floor swept the night before? Well, he has diabetes, so his foot is permanently bleeding for some reason. What's that? Some douche at a restaurant (or something I forget the details) thought it'd be funny to stick a thumbtack in a random person's shoe? Turns out it's my friend's shoe, and now BOTH his feet are perma-bleeding. Get falsely accused of rape twice by semi-random random people (one was someone whose cosplay post he liked on facebook, the other was a woman he chatted with for 2 minutes at a convention) and get in the newspapers? Yup, although in that case at least he was lucky enough to have an airtight alibi both times (first time, he was in the hospital in another city at the time, impossible for him to have done it. Second time, he had video proof that he was streaming Cards against humanity on Twitch with 4 friends at the time). Playing XCOM:EU on easy? Miss 80% of shots above 80% in the first 3 missions, everyone dies, this happens 4 times, he gives up on the game because the RNG hates him. He decides to clean the house he lives in with friends? Well, the broom just HAPPENS to break on him and cut his arm when HE uses it. And so on and so on. :s I feel pretty bad for the guy. It's just not funny how shit his luck is.
So yeah, there are some things that can't really be explained by just your environment (although that and the people you surround yourself with does have a huge impact on your life). Sometimes, shit just happens for no adequately explainable reason. That's luck. And everyone I've met has a different kind of luck.