Are there any differences between "has not to be" and "does not have to be"?
if you check the list, the list has not to be empty.
if you check the list, the list does not have to be empty.
Here, have is used to expressing obligation. In this usage have is not an auxiliary verb, so you can't negate it directly. Instead, you need to insert the meaningless auxiliary verb do and negate that:
The list has to be empty.
The list does have to be empty.
The list doesn't have to be empty.
Writing "The list has not to be empty" is like writing "The child walks not to the store". People don't talk that way anymore, so it sounds archaic.
Although the answers by snailplane and Bob Rodes are correct, as far as they go, I have to add that what is involved here is neither the auxiliary verb have,has,had,having ... nor the lexical verb have,has,had,having ... but a new ‘semi-modal verb’ which has evolved over the last hundred and fifty years or so.
Auxiliary HAVE: I have finished.
Lexical HAVE: That is all I have to say.
Semi-modal HAVE to: I have to stop now.
For historical reasons this verb is still spelled have to,has to,had to; but it is in fact a single word, pronounced “hafta/hasta/hadta” (/hæftə/,/hæstə/,/hædtə/,/hævɪŋtə/). The have piece and the to piece are inseparable.
The expression appears to have arisen in spoken English, and it has not yet been totally integrated into the formal dialect—consider Bob Rodes’ characterization of has to not be as a “split infinitive” according to traditional canons. Older texts could still treat the emerging expression as a ‘construction’ built on have rather than the ‘word’ which it has become; and because such texts are still part of our living culture they act as models for many present-day writers working in high-formal modes. This gives rise to constructions such as your own first example or Bob Rodes’ “I see you haven't to go to detention today”. These are accepted in formal registers—it is possible that they may actually be required in some circles, though I think we have by now gotten beyond that. But they are impossible in colloquial registers.
Obviously you have to be able to understand the old-fashioned constructions, because you will encounter them in your reading. But I advise you to avoid them in your own writing and speech. Use the forms recommended by snailplane (spelled the established way), or use must/need not/must not where hafta/don’t hafta/hafta not feel too colloquial.
As snailplane says, "has not to be" is archaic. However, we will still sometimes say "The list has to not be empty". (Technically, this is a "split infinitive" and is not considered "good" speech, but nevertheless you will hear it from time to time.) In this case, the meaning is different: it means the list can't be (or mustn't be) empty. We would typically use one of those verbs (can't or mustn't) in this case.
The difference in meaning between "the list does not have to be empty" and "the list must not be empty" is that in the first case, the list is not required to be empty (it may either be empty or not), and in the second case, it is not permitted to be empty.
Edit: as I mull over my comment to the next answer, I recall one of my British schoolmasters (circa 1971) saying "I see you haven't to go to detention today, Rodes; now there's a surprise." In this case, it had the meaning of non-requirement rather than non-permission, so it would seem that the difference in meaning can vary regionally. "You have to not go to detention" is something that an American might say (again, not typically) and mean that you must not go. "You haven't to go to detention" is something a Brit might say (Americans would say "you don't have to go to detention") and would mean that it is not required that you go.
Your first sentence is not correct as a negative sentence should be made using an auxiliary verb.
For this reason you should use the second sentence: 'The list does not have to be empty.’ or the contracted form: 'The list doesn't have to be empty’.