Often, I come across expressions like 'I can't have no money', 'I don't want no help', 'Do you want them tomatoes', 'Be careful with them toes' when watching cartoons, movies and shows. Does anybody consider these to be proper English?
None are correct English, but they are typical in the vernacular. These particular examples are often used by Cockneys (people from east London), where double negatives are common, often for comical effect (in the form of irony or sarcasm) or to emphasise.
I can't have no money, I don't want no help
More frequently "I ain't got no money". Negating the fact reinforces the speaker's lack of money / complete refusal of help.
In a sarcastic vein, a Cockney would say:
D'ya see Andy's new bird? No slim chick!
Andrew has a new girlfriend. She's very fat.
Do you want them tomatoes? Be careful with them toes
I don't know the origin of these deliberate errors (them instead of those), but I suspect that they are a way to identify oneself as a member of the community. Another common deliberate mistake is to decline the verb "be" as if it were regular:
We was waiting for the bloke, an' 'e never came!
They're definitely improper, but they're often considered acceptable in very informal situations.
"I can't have no money" - This is an example of negative concord which is common in African American Vernacular English. Its meaning is not emphatic, the extra negative words actually agree with the first negative (n't in this case) just like "any" in a standard English sentence: "I can't have any money"
I don't know about "Do you want them tomatoes" specifically but it seems like "them" is replacing "those" which isn't too crazy.
The important part is that there's no such thing as speaking "incorrectly" if you're a native speaker. Native fluency is the definition of your language, anything a native speaker says intentionally (not mistakes) is acceptable.
The first two aren't grammatically wrong, they just don't say what people typically mean when they say them.
They aren't proper English, no. If you think about:
I don't have no money.
it actually means 'I have money'; it's an example of a double negative, and as such means the exact opposite of what the speaker wanted to convey.