I think it's pretty normal, I mean, most living beings don't really have a purpose of living.
And nah, I mean, that's really up to you, but I think it's not worth commiting suicide over no having purpose on life, I can understand why would that be a reason, but not everyone needs one, it would be kinda shitty if fate existed and each and every one of use were created with the single purpose of doing an specific time, when you think about it, it sounds absurd.
So, I think there's no really a purpose or reason for anyone to be alive, that doesn't mean that everyone should die, I wish people die but that's because we are kinda mean but that's other topic.
In the end is up to you, to decide what to do with your life, heck even that can be your purpose, just going for the ride.
I think that even the people that think they have a reason, are probably incorrect.