Just so you know, sometimes textbook Japanese goes out the window in real life situations.
クラスに入っていただきました -
They're being polite.... it's the same as "were they/you in class"
いろいろなことを知っているって言うこと -
Someone said they know various things. As far as I can tell "iu koto"
basically means "kind of thing"..... like "dou iu imi" means "what
kind of meaning?" and "sou iu koto" means "that kind of thing".
生まれたのも育つのも京都なんですよ -
Ok a lot of your questions involve の, and as far as I can tell most
of them can be solved by a simple explanation.
の is possessive. As in "watashi no neko" (my cat). But if "cat" is
mentioned previously or if it's obvious what you're talking about,
all you need to say is "watashi no". Also, の is used at the end of
a verb to make it into a noun. You would never say "oyogu ga
suki". You would say "oyogu no ga suki" (I like swimming).
So in this sentence it's saying "I was born and raised in
Kyouto". Umareta and soudatsu are born and raised. The の is there to
make the verbs into nouns.
私が生まれたのは高山と言う町です -
In this sentence the の is a placeholder for the word "machi". "I was
born in a town called Takayama."
はず -
I think if you say something that hasn't happened yet it might be
okay to say 「はず」. Like "konban benkyousuru hazu desu" means "I am
supposed to study tonight". But if you said "yuube benkyousuru hazu
desu" (Last night I was supposed to study) it implies that last night
you did NOT study.