word usage - There are no ~ / There are not ~

All I know about "NO" is like this.

There are no movies playing on Christmas day.

=>There are not any movies playing on Christmas day.

=>We won't be showing any movies on Christmas day.

And here's what I'd like to ask.

As I don't want to wast my time doing nothing at home, I usually make my way to a place where I can do something productive.

1. 
   

   So, there are not many things that I do at home.

   
   


2. 
   

   So, there are no many things that I do at home.

   
   
   

Here, I think #1 is right because #2 means "there are not any many things that I do at home" and this sounds awkward and not grammatically right. Am I right to think this way?

Answer

No is a quantifier, like one, some, many, much, few, three. We don't combine quantifiers except in mathematical expressions (one hundred, three dozen)^†, so no many is illegitimate.

Not is a negator. It can be combined with quantifiers (not much, not one) and other word classes (not difficult, not quickly, not a question). Generally, however, we prefer to 'raise' the negator in a predicate and attach it to the verb, just as we prefer to 'raise' it out of a subordinate clause into a main clause. The unraised versions tend to be employed only to emphasize where exactly the negation lies.

^∗ We will be showing not any movies on Christmas day.
^okWe will not be showing any movies on Christmas day.

^? I think that we won't be showing any movies on Christmas day.
^okI don't think that we will be showing any movies on Christmas day.

---

^† You will see expressions like No three of them could lift the rock. Here no doesn't combine with three, it quantifies the entire following NP; that is, this sentence is equivalent to "No set of three of them could lift the rock".