The last one didn't get my changes or thiago's
Single negative applied to a combination joined by or.
The last one didn't get either my changes or thiago's
As above, but using either to make it clearer what the or is joining.
The last one got neither my changes nor thiago's
Made negative by neither...nor.
The last one didn't get either of my or thiago's changes.
The last one got neither of my nor thiago's changes.
Another approach to the same thing, using either...or and neither...nor slightly differently.
The last one didn't get my changes, nor thiago's.
Nor used without neither. This is rarer, though it can happen when speaking because you add it as an afterthought.
Note that all of these variants either use didn't or use neither, but none of them use both as yours did.
First, mistakes. Get that out of the way:
Could you explain me please when I should use "to", "to the" or no one of these, there also was explained that "the" is never used with home or school.
Explain to me...
Should use neither of, if two choices or none of, if more than two.
Okay, now the question. It's a good one.
Where using a word to refer to a class or category of place, like school or home, you don't use the article.
"I go to school five days a week." "When I go home, I pass by the airport."
When referring to a specific building, the article is used.
"Can you tell me where the school is?"
Also, titles of institutions often contain articles and these should be used when referring to them.
"I studied at The London School of Economics."
Home is almost always used generally, but there are exceptions.
"The dog was sent to a home for stray animals." "He comes from a good home." "Canada is the home of cajun cooking."
Airport is always used with an article.
"Take me to the airport."
Airport is never used to refer to a class or category. You wouldn't say,
"When in airport, never leave baggage unattended"
but you could say,
"He went to school to be an air traffic controller"
"Don't leave your passport at home when you go to the airport."
Best Answer
What do you notice that is different between your examples?
Allow me to give a different example:
Are you seeing it? It's the possessive your. What happens when you throw that possessive in? Home goes from being an adverb (modifying go), to a noun which forms a part of an adverbial prepositional phrase. (I don't believe it fits the definition of the indirect object the going is not happening to the house, but rather toward it. Perhaps I'm wrong here.)
Home is a rare word that forms an adverb in this form.
On its own, your home isn't typically used as an adverbial phrase to modify go. Instead we make it part of the prepositional phrase to your home because it explains the action of going.