I have my daughter who has cartoon characters on her drinking cups, packed lunch box etc... Is this permmited?.
The pictures that are found on drinking cups and food containers do not come under the ruling on images that are forbidden, because these are items that are used and abused, but it is better to avoid these vessels and containers so that the child will not become attached to cartoon pictures and symbols. Some children become very fond of a particular image that they want to have on their bags, pencil cases and cups, but this has a negative impact on the child and makes him fond of imaginary characters whose conduct is not free of things that are forbidden in Islam.
Shaykh Ibn ‘Uthaymeen said in al-Sharh al-Mumti‘ (2/206): It has become very common nowadays to have pictures on almost everything, so these pictures are found on plates and dishes, food containers, in books and magazines; they found in everything except what Allah wills (should remain free of them), and there are also images that are eaten, such as biscuits in the shape of fish or rabbits.
We say: Keeping them because of the pictures or images in them is undoubtedly haraam. Buying magazines in which pictures are published for the sake of the pictures is also haraam, but if it is for knowledge or information or to read the news, then we hope that there is nothing wrong with that, because of difficulty (in avoiding it completely). Allah, may He be exalted, says (interpretation of the meaning): “and [Allaah] has not laid upon you in religion any hardship” [al-Hajj 22:78]. These images are not what the person is seeking when he buys it and he does not care about them. This is also the case with regard to dishes and plates and food containers and the like. And it may be said that they are treated with some level of disrespect so they do not come under the category that is haraam. End quote.
And Allah knows best.