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I wasn't taught how to form a tag question when the main sentence involves "no". Is it grammatical to say
There's no problem with the car, is there?
There's no apples left in the carton, are there?
The poor man has nowhere to go, does he?
Nobody cares about it, does anybody?
It has nothing to do with the incident, does it?
Nothing is as precious as unobtainium, is anything?
(Some of the above examples might not sound natural. It would be great if you could suggest me better alternatives.)
The Original Poster has the right idea about the grammar here. When we have negative sentences, the question tags must be positive, not negative.
One small, but important point though: usually, we can only use basic personal pronouns in question tags (I, she, he, it, we, you, they, there). We don't normally use compound pronouns such as:
With the words ending in -body or -one, we normally use the pronoun they:
If we know that we are only thinking about males or females we very occasionally use he or she, but this is quite rare.
When we use the pronouns ending in -thing, we normally use the personal pronoun it in the tag:
The Original Poster's examples
The Original Poster's examples are all fine apart from the ones using the pronouns nobody and nothing. These would be better like this:
Nobody cares about it, do they?
Nothing is as precious as unobtainium, is it?
There's no problem with the car, is there?
There is/are no apples left in the carton, are there?
The poor man has nowhere to go, does he?
Nobody cares about it, do they?
It has nothing to do with the incident, does it?
Nothing is as precious as unobtainium, is it?
Nobody has been told, have they?
Everybody is ready to leave now, aren't they?
Open the door, will you? ( Won't you /Can you/ Can't you) Imperatives
Let's (not) go there today, shall we?
She almost never studied, did she?
I don't believe you've paid for it yet, have you?
This/ That suit is expensive, isn't it?
I'm right, aren't I?
She scarcely cares, does she?
