Well actually you wrote pretty little.
I'd say that if there are suicidal thoughts then it's a fantasy of not being able to cope with the problems around oneself. It's actually not that big of a deal when talking about youths, since in puberty there is a huge change in our psyche, which adds to the problems already there.
Suicide in youth can be due to various reasons, but which are all painful to the individual. It's possible, for example, that childhood experiences now evolve again into the conscious mind which had been repressed before. It's particularly significant, because the young people now achieve full maturity and realize that they are now themselves actors of their own lives and the lives of others - not at last because of their sexual drive and the possibility to live it.
There arises a complete new feeling. It may be helpful to remember how you felt and imagine different situations where there might be problems.
So one reason can be repressed thoughts and feelings, which arise now and above all interfere with the sexuality of the individual. The individual might notice that it's not able to have a "good" sexual life. It's possible that there might be a tension between the revenge thoughts and feelings of the Id, which is in contradiction to the Super-Ego. The individual might feel that it's treated unjust in some way, but rather take its own life before the life of others, who are not to be blamed. Or it might feel worthless to society.
The main focus should be the relationship between the adolescent and its parents or substitutes of them. The question is: Why should somebody actually feel that this world is bad and doesn't have any good things? The feeling behind suicide is that oneself is not needed or that oneself can not become happy. Why not become happy? Since the adolescent is not ready to be an adult.
So I would ask myself what it means to be an adult and what it means for an adolescent. And I'd look what there might have been in childhood which prevents the adolescent to finally become an adult. I'd also look at some statistics, for example if the rate of suicide is higher among girls or boys and then (cautiously) draw conclusions.
I think it's a matter of how close the family member was to the adolescent and in which age the individual was at the time of death of the family member. It's probably also a matter of how the individual receives that the family member is gone. It may well be that it's harder for a child if the family member kills itself when the child is already older - since it has more consciousness and it knows the person for a longer time. I think it's also an important question of how guilty the child feels about the loss of the family member.
There are a lot of other questions to be considered, here only a few points of departure. I hope I could help you.
greetings