Using "neither" can be tricky, so in general, you can stick with "either" and never use "neither". Even native speakers frequently use it a way that goes against formal grammar rules.
Your first example is fine, and again you can stick with using "either" this way, even if the context is negative.
For lunch I'm either going to have spaghetti, or I'm not going to eat at all.
As in your second example, the "standard" way ensure you use neither correctly is to pair it with "nor". Just like you would use "either ... or" to create a list or choice, you can use "neither ... nor" to create a negative list (or lack of choice).
For lunch I'm going to have either spaghetti or a sandwich.
For lunch I'm going to have neither spaghetti nor a sandwich.
Your third sentence is an example of vernacular -- this construction shows up in various dialects, but it's not "formal" English and so I would recommend against using it. However, the only thing wrong with it is where you place the "neither", which should be in the middle, and you have to reorder the subject/verb pair:
I am not going to hurt you, but neither am I not going to protect you.
I don't know if there is any actual rule for this. It may just be another English structure that you can memorize and use as needed. Other examples:
I'm not going to have spaghetti for lunch, but neither will I have a sandwich.
She isn't at home, but neither is she out on a date, so I don't know where she is.
It's New Years Eve! I haven't been invited to any parties, but neither am I just going to stay home. I think I'll go find a nice crowded bar and celebrate there.
In Standard English, options 1 and 3 are grammatical; option 2 is not.
In "standard" dialects of English, neither is only used in affirmative constructions.* You cannot say, "I don't like neither this nor that." You must say, "I don't like either this or that" or "I like neither this nor that."
And this starts to show why the statement "either or means XOR" is not necessarily true.
If either or were truly XOR, "I don't like either A or B" would mean either I like both A and B, or I dislike both A and B. But no one would ever use this sentence to mean I like both A and B.
And so, we might be tempted to say not either or means NOR (not A and not B), but I suspect this is also not always true. The fact is, outside of certain technical contexts, the words or and and cannot be consistently mapped to logical operations.
Fortunately, this also means that we potentially have more ways of expressing the point. For example, in addition to options 1 and 3, and other contributors' suggestions ("There is no solution for either A or B)", you could try:
- There is no solution for A. There is no solution for B.
- There is no solution for A and there is no solution for B.
- Neither A nor B has a solution.
- Neither one has a solution. Not A. Not B.
- Neither one has a solution. Not A and not B.
- There are no solutions to these problems.
- A has no solution and B has no solution.
- and on and on and on...
*There are "nonstandard" dialects of English where this kind of double negative is used with a negative meaning. That is, in dialectical English "I don't like neither of them" means the same thing as Standard English's "I don't like either of them." This dialectical feature is called negative concord. It's not a mistake, nor is it ungrammatical in the dialects that use it.
Best Answer
Yes, the usage of "neither... nor" is natural in this sentence. There is a grammatical mistake however, as "procrastinator" needs an article-- specifically, it needs to be "a procrastinator" here.
The reverse order would also work.
Content-wise, I am skeptical that "not being a procrastinator" is addressed in the following sentence... scheduling things and planning the day have nothing to do with procrastination. That said, it's still a natural sentence, and would be idiomatic to a native or fluent speaker.