Learn Polish: Nowa maszyna działa ciszej. - The new machine runs more quietly.

To form the comparative of a regular adverb, you typically drop the final vowel and add -ej. Here, the base adverb is cicho (quietly). When adding -ej, the consonant ch mutates into sz, which is a common sound change in Polish. This gives us ciszej (more quietly).

In English we can say it 'runs quieter'. Could I use ciszej to say 'a quieter machine'?

No, ciszej is an adverb, so it only describes actions (verbs). If you want to describe a noun (like a machine), you need an adjective. 'A quieter machine' would use the feminine comparative adjective: cichsza maszyna.

Why does the Polish sentence use działa instead of a word for 'runs'?

The verb działać means 'to function' or 'to work'. In Polish, machines 'work' or 'function' rather than 'run'. If you used the Polish verb for physical running (biec), it would sound like the machine grew legs and sprinted away!

Based on this lesson, how would I say the machine runs 'the most quietly'?

Once you know the comparative form, the superlative ('the most...') is very simple. You just add the prefix naj- to the comparative adverb. So, ciszej becomes najciszej (the most quietly).