"a lot of" for countable nouns

[Steve88]

I've the following questions and please answer for me, possibly with explaination:

1. Can we use "a lot of " for countable nouns like a lot of crows or a lot of cups?

2. Which is the right way to say: "There are a lot of crows." or "There is a lot of crows."

3. Do we say "There are a basketball court, a badminton court and a football field." or "There is a basketball court, a badminton court and a football field."?

[Jamie (K)]