My husband killed himself many years ago leaving me and my 2 children, aged under 5. It was an absolutely appalling time but I decided that for my children's sake I had to do everything possible to make their life as normal as I possibly could. Luckily I was able to move near my parents who gave us all invaluable support and my father was a wonderful male role model to them. I also chose not to have any further relationships so I could devote my life to them and for them not to have to deal with any more changes in their lives than they'd already experienced.
Both were teased at primary school about having a dead father, fortunately the school was right onto it and dealt with it very well. We didn't really talk about it although I always said I was happy to answer any questions. At about 16 the younger one decided they wanted to know everything about what had happened so I did explain, it seemed to help them. The older one did not want to know and has never asked.
Very luckily, they have both grown up to be happy, well adjusted, empathetic, successful people who have both married wonderful people and are very content with their lives. Of course it had an impact on them, how could it not, losing a parent in any way is bound to. But the death of a parent doesn't automatically mean the children's lives will be dreadful and they will suffer from poor mental health.
One of my children actually says that it has an effect on him in a positive way, in that he always pushed himself to do well at school and aimed high, because he never wanted anyone to say "look at x, what a loser, but it's because he's got a single mother and is the child of a father who killed himself". He is very ambitious and that's led to his very successful career, who knows whether he would have achieved that anyway, it's impossible to say.