Like most nouns, 'newspaper' can be either countable or uncountable, depending on the meaning intended. For example, if you say 'I bought a newspaper' you are talking about a single object , so it is countable. But if you say 'Put some newspaper inside your wet shoes and they'll be dry by morning' you are thinking of newspaper as a material or substance, so it's uncountable. The same goes for ice cream. If you ask for 'an ice cream' you are imagining a single object - probably in a cone, and this is countable - one ice cream, two ice creams, three ice creams. But if you're at home, or in a restaurant, where you'd have a few spoonfuls of ice cream in a bowl , then you'd probably say 'some ice cream'. In this case, it is uncountable because you are referring to a certain amount of a substance, as opposed to an individual item.

"Newspaper " is countable. You can have 3 newspapers. The paper it is printed on, called "newsprint" is not countable. "Ice cream" is not really countable, but you will occasionally hear "they have three ice creams", meaning three types of ice cream. Generally you count the container the ice cream is in: two dishes of ice cream, four ice cream cones.

Can you give an example where you think "newspaper" is uncountable? It's possible you just misinterpreted the sentence.

Countable you can ask a question how many ice cream do you want