/jp/ - Otaku Culture

http://www.guidetojapanese.org/learn/grammar/particlesintro_ex
Could someone give me a quick explanation on what I'm not understanding here?
Wouldn't it be 「が」and then「は」(the other way around) on the first one, since it Jimu is trying to figure out who Arisu is and Bobu already knows it?
And in the next one, wouldn't the first one be 「は」for similar reasons?
I also don't get why there's a 「が」on the second one in the last section when Bobu seems to know about the library in question.