> Why does anything exist?
No reason. It just exists.
> Actually, DOES anything exist?
Yes, obviously.
> What is real? What is fake? Is time an illusion?
We merely call real the parts of ``what there is'' which are (conceptually) solid and durable enough to our taste or easy to grasp. So, physical reality is generally considered more real than dreams. Note that a sufficiently advanced dream could essentially become reality. However, it is usually clear even when dreaming that physical reality forms the basis of dreams.
Time is not an illusion, but the passing of time is. Past and future are not any less real than the present.
> Is reality an illusion? Is it a simulation?
Reality is not an illusion, by definition. Is it a simulation? I don't know.
> If things do exist, does there need to be a reason why? Or can things exist for no reason?
No and yes.
> What is nothingness like? What is death like?
Nothingness does not exist, there is only an idea of nothingness, just like luck does not exist and we only have an idea of what it is.
As for the experience of death (beyond the moments of transition), obviously when you die you can choose to linger as a ghost, resurrect (for casuals) or create a new character.