>What happened to the Princess of the Crystal? Why did she come here in the first place?
Princes of the Crystal is Momoka. She came to stop Sanetoshi's terrorism. It's a fight she's willing to fight even after dying for it.
>What is the Penguindrum anyway? Is it a mere concept of fate and bonding or something else?
That's the hardest question of this anime really, the rest of the plot is pretty straightfoward. One could argue it is family bonds, or fate. Personally, I never thought about it, and I think it isn't relevant. Even Momoka couldn't find words to explain it, if i'm recalling it right.
Also, some stuff to think about:
Sanetoshi wasn't a "bad" guy. He wanted to alert the society to the existence of the Child Broiler. His ways of action were bad, terrorism is never the answer. But I can sympathize with the guy. He was fighting a hard fight for the greater good. Was he really the "bad" guy, or was he the good guy and the main characters did wrong to stop him?
About the Child Broiler, what is it: It's a place where unwanted children go and are made "invisible", which I interpret as a metaphorical place that holds all the unfavoured children, be it untalented or abandoned, and where they are made "invisible", that is, invisible to the world. This invisibility is not being relevant, being scum, being poor, being unemployed, being ignored, it is being what society tries to hide and make invisible. In Penguindrum, this process is treated as, a single moment and boom, you're irrelevant for the rest of your life. This in real life, obviously, is a slow process, but here is shown as a single moment process. From one moment to another, you stop mattering to the world. Also, this is the part that hit me the most in the show. It's incredibly realistic if you think about it. Rich children are born rich, talented children are born talented, and will always be visible. The unwanted are invisible.
Feel free to ask whatever, I love debating Penguindrum.