A sentence becomes negative by specific words. Most of those have 'no' in it. For example
No
Nobody
No one
Never
Not
Nowhere
...
And yes a sentence without a subject can be negative. Here's an example:
Stop the car! -- positive
Do not stop the car! -- negative
Do your homework!
Don't do drugs!
Native English speakers use going to and will interchangeably in many sentences, even sometimes when the events are (or are not) planned in advance. For example, both "the fireworks will start at 7pm tomorrow" and "the fireworks are going to start at 7pm tomorrow" are perfectly fine, even though it's clear they've been planned well in advance.
So it's tough figuring out these differences in meaning.
I have found a context that makes some of these differences in meaning clear to me. I can't say which other contexts these differences carry over to.
I can't watch the movie with you; I'm going to eat out this evening.
Here, it sounds to me like the dinner was planned in advance.
I can't watch the movie with you; I will eat out this evening.
This sounds rather rude to me, because it doesn't sound like the dinner was planned in advance.
I can't watch the movie with you; I eat out this evening.
Here, the simple present sounds to me like habitual action: the speaker eats out every Monday evening.
I can't watch the movie with you; I'm eating out this evening.
Again, the dinner sounds like it was probably planned in advance.
However, simple present continuous doesn't necessarily mean an event has been planned in advance. Both of the following are perfectly fine, and mean the same thing.
It sounds to me like you really need help; I'll come over right after work.
It sounds to me like you really need help; I'm coming over right after work.
The negative of these constructions behaves more or less like the positive. You don't have to have other plans to use "I'm not going to eat out this evening." You can use it if you just aren't planning to eat out. For example, you could say:
I'll be at home at 8:00 if you want to telephone me then; I'm not going to eat out this evening."
Best Answer
You are right that it is not gramatically correct, but certainly in British English it is quite commonly used. It is a double negative, which if we would take literally would mean a positive. But in fact we don't take it literally, and the meaning which it still conveys is
I would argue that the reason it is used in the Pink Floyd song, is for irony. This is because using no instead of any in a sentence like this, is considered to be something someone uneducated would do. You certainly wouldn't hear the Queen saying it like this!
Also, maybe the single-syllabled "no" just works better for the rhythm than "any".
Not obeying the rules of grammar, in some circles, makes one appear outrageously cool and hip to one's peers. In civilised England however, we recognise that speaking and writing grammatically is more important than anything else in the world.