1 (おまえは)大学になんか行けやしないよ。(colloquial, a bit strong words)
= You won't be able to go to college. (Because you aren’t so smart or something like that)
なんか would emphasize 大学 and (行け)やしないよ is emphasized negative form in colloquial style.
2 おまえだって。(colloquial)
= Says you! (You are nothing different from me)
When you want to say that it’s not only you, you can use だって.
あなただって、あの人だって、先生だって、大人だってetc…
3 行くの行かないのと~
>what is the meaning of と?
In this case, you could take it as a abbreviation of とか言いながら or などと言って.
行くの行かないの(とか言いながら)迷ってる。
死ぬの生きるの(などと言って)騒いでる。
4 何が食べたいですか?
= What do you want to eat?
何が食べたいんですか?
= What exactly do you want to eat?
>here んcan be replaced by の?
Yes. But it sounds a little stiff.
5 行くなら 行くのなら
>what is the difference ?
It’s the same.
>のcan be replaced by ん?
Yes. But it would be quite casual.
6 もっと話をしていたい。
= I want to talk more with you. And I hope this situation keeps going.
もっと話をしたい。
= I want to talk more with you.
7 取引先に~
> what is に?
In this case, it would indicate the place.
どこ(に)行くの?
取引先(に)行きます。