"There are" is the correct one, but you might hear "There's" or "There is" even from native people. Consider it as an informal way of telling the same thing.

It all depends on what you mean by 'correct', Alexandra! Language is not an exact science, and language changes. Native speakers say 'There's a lot' because it's easier to say than 'There are', and also because it sounds right, and because other native speakers say it. It's a more colloquial form, but personally, I don't consider it to be a mistake, as such.

There are a lot of people is the correct one. Maybe people use "there is" because they see "A lot of " and that "a" is what makes them use "there is". Let's see if any native speaker tells us if using "there is" is also correct ;)

I use there are. "There are alot of ppl" Saying "there is" I guess is another way someone might say, "there's alot of ppl"