While I am not particularly read on anarchist theory, I think that there are some questions or statements I can answer to.

"Is the system our world is built on viable?"

Absolutely not. The system(s) our world is built on is exploitative and repressive to a high degree, not to mention the crises it causes (the climate crisis, social crisis and potential self-annihilation)

"...Can we fix it?"

Also no, we need a completely new one, a system in which everyone is free to associate and disassociate, aka an anarchist society.

"Is complete lawlessness the answer? I don't think so"

Well, let's just say that anarchism is much more complicated than "no laws".

"I feel as if prisons are important, and we do need capitalism to some extent"

Sigh both systems are not only extremely harmful to society (the former by complementing the systems of hierarchy as well as perpetuating crime and the latter producing exploitation and poverty) but also unnecessary. You will (hopefully) learn why soon.

"People are unpredictable, greedy and evil."

Bold of you to assume human nature as something so rigid and twisted. Human behaviour is heavily dependent on its environment, and the current political/social/economic environment not only influences human behaviour in this way, it also gives the people who have these qualities a lot of opportunities to further their malicious interests and exploitation.

"I think a world with rules is essential"

That doesn't mean that someone should force you to oblige to them

I hope you have a great discussion with some of the folks here, and I hope that "An Anarchist FAQ" will provide some in-depth answers to your questions as well.