You are right that 'clothes' is always plural.
Clothing is always uncountable. It has no plural form, and cannot be used with an article. You can say 'waterproof clothing' without an article, and you can use 'some' with 'clothing'. For example; 'Students must bring waterproof clothing on the trip'. If you really want to use the article 'a' here, you would have to say 'a waterproof coat' for example, or if you want to be more general about the type of clothing, you could say 'a waterproof garment'.
'Garment' is the only word in this semantic group - with the general meaning of 'clothing' - which is a countable word with a singular form.
Yes ,'cloth' is a synonym of material or fabric, and is usually uncountable. It's just about possible to say 'that's a nice cloth' or 'the designer showed me some different cloths', but it sounds a little strange. We'd be more likely to say 'a type of cloth' (singular) or 'types of cloth' (plural).