I have send some caricatures to a newspaper...?

Question

And they have accepted to publish them on their magazine.

Shall I demand some money for that or not?

If so, how much money I should demand per month/1caricature?

Answer 1

What terms did you include with the pictures?
I am guessing none!

Under what terms do they accept unsolicited material?
This can usually be found somewhere in the publication. If not try their website.

How do you know they were accepted for publication?
If you have received a letter or email, contact the person/dept that sent it.

Check them in The Artist's Yearbook (local library). Their entry will probably have some sort of guide as to their payment rates.

Payment is not normally made until after publication. However, if they have not used your pictures within a "reasonable" time you can ask for their return. "Reasonable" is defined differently depending on the editorial lead time of the publication.