1) a)
急 modifies カーブ in 急カーブ. It expresses the curve / turn is sharp. On the other hand, 急に modifies 切り. It's temporal; unexpectedly or immediately.
b)
~と反対
opposite to
2)
That's right.
3) a)
It's a variation of ませ, which is the imperative of ます. (Have you seen いらっしゃいませ, お帰りなさいませ, お休みなさいませ or like that?) まし (and いなさる(かね)) shows that the speaker is an old person and from rural area. (but not crude, he/she is polite.)
b)
Yes, it's いる + なさる. You can think it's いらっしゃる.
4)
The latter sounds more colloquial.