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Для второго случая представьте контекстююю

imho
Wholesale Health & Beauty Products

'Health and beauty' is the set expression used:

http://goo.gl/ScuCu8

'Supply of ......' is the standard expression in English, as it implies 'supplying of ......' -- the activity, ie "that's what we do". The word-for-word translation 'SuppliEs' (in the plural) can't be used in the same way -- it doesn't have the same (verbal) meaning.

Alternatively you can say 'SupplieRs of .......' or '...... SupplieRs'. In fact, if anything, 'SupplieRs' sounds slightly better.

WHOLESALE BEAUTY SUPPLIES - DISCOUNT HEALTH AND BEAUTY SUPPLIES

Exactly. That's the difference between 'Supply of x' and 'Supplies of x'. The first means 'The supplying of x [to customers]', while the second can mean this, but usually just means 'Stocks/quantities of x'. And 'supplies' as used in your Amazon example just means 'products' -- not the supplying of them.

Business cards are to tell people who you are, and what you/your company does. You wouldn't put just 'Stocks/quantities of beauty products' on a business card, would you?

I would use either 'Supplier of Health & Beauty Products' or 'Health & Beauty Product Supplier' (it doesn't matter which). That way you avoid any ambiguity. Use 'Supplier' if it's a single person, 'Suppliers' (pl.) if it's a company.