grammaticality - there is a lot or there are a lot? over here or at here?

In addition to other reasons given, it's singular because English speakers don't like putting multiple (unstressed) R sounds in a row; "there is" or "there's" is easier to say than "there are".

It's very common to hear things like "There's over a hundred people in here!" or "There's too many to count"; grammatically, those should have are instead of is, but when you're actually pronouncing the sentence, "There're" just doesn't roll off the tongue smoothly, and "there's" is just as understandable, so the substitution is made naturally and frequently.

In situations where the word "are" is more emphasized, it will be used much more readily:

There are ways to get what you want

With this sentence, normally "There", "are" and "ways" are all pretty equally stressed during pronunciation.

Compare that to

There's loads of ways to get what you want.

With this sentence, "There's" is relatively unstressed, and "loads" is heavily stressed. Because of this stress pattern, "there's" will often be said instead of "there are".