The point of this list is to show you that some nouns have BOTH countable and uncountable versions. It might be helpful to think about "countable" and "almost uncountable"! When we talk about "hair" on someone's head we normally think of it as uncountable, because it would be extremely difficult to count each individual hair. We use the countable form In examples like "The police found three blonde hairs at the crime scene.". So your example your sentence is grammatically correct, but it would be extremely unusual for anyone to use it. We'd say "doesn't have much hair." 'Cake' is used in the uncountable form to refer to the general class of thing which can be called 'cake'. For example "I like to eat cake." AND the countable form for specific items. For example "Normally my wife bakes a cake (1 cake) every Saturday, but today she baked two cakes!" "Beer" is normally uncountable because it is a liquid, and so we need to say "glasses of beer/litres of beer/etc", but it CAN be used instead of the phrase "different types of beer". For example "At the festival I tasted three beers and two wines." Because it's possible to identify and count different types of most types of food and drink we CAN use nouns that are usually uncountable in a countable way. For example "The farm produces three cheeses." BUT often people prefer to say "types of/brands of/makes of,etc"

Many of these could be either, depending on how they are being used. Beer for example: 1. How much beer did you drink? (Uncountable) 2. How many beers do you have on tap? (Countable=how many different types/brands of beer do you have)

They are uncountable.

You can use "hairs" as countable as you did in the example. "My mother is getting a few grey hairs now" could be another example. "Cakes" and "beers" are countable, too. However, "Advice" is uncountable; we say a piece of advice (not ‘an advice’) and some advice (not ‘some advices’). :)