Is it legal for the landlord to ask a liquor store owner if I bought anythig to call them. Also, I had people I do not know followed me. When the doorman saw I was leaving the building, instead of opening the door, he picked up the telephone and stared. I just went out. I met my friend and I saw the doorman from across the street, which is a hotel looking into stores when I went around the corner.
I am new in the building and paying low income rent.

There's nothing illegal about it. If he ever does something with any information he learns about you, that might possibly be illegal, but until that day there is nothing you can do.
Is there something about how you got the apartment that might make him suspicious of whether you were qualified?
Is it city, state, or federal housing? Is it elder/disabled, Section 8, or just low income?
Not that we really need to know, but something might explain why this is happening.

It is not illegal. If you are being rent subsidized, the landlord may be concerned about his property.

How do you know about this?

Assuming it is true ( and I personally doubt it) no it is not illegal,

But why would they be doing this