Learn Polish: Im więcej, tym lepiej.

This is the Polish equivalent of the English 'the ..., the ...' structure. Im starts the condition (the more), and tym introduces the result (the better). Both must be immediately followed by a word in its comparative form, like the adverbs więcej (more) and lepiej (better).

Why do we use the adverbs więcej and lepiej instead of adjectives like większy (bigger) and lepszy (better)?

Because this is a general, abstract statement that doesn't describe a specific noun. When you are just expressing that a situation is better in a general sense, Polish uses adverbs. If you were talking about a specific noun, you would use adjectives, like in the sentence Im większy dom, tym lepszy (The bigger the house, the better).

Is there a missing verb in this sentence?

Yes! Just like in the English translation 'The more, the better', the verb jest (is) is understood but completely dropped. If you included it, it would be Im więcej jest, tym jest lepiej, but leaving it out is much more natural for this common saying.

Could I swap the order and say Tym lepiej, im więcej?

Yes, you can! The meaning remains the same, but the emphasis changes slightly, much like saying 'It is better the more there is' in English. However, starting with Im is the most standard way to express this.