Learn Polish: Ten uczeń jest uważny i słucha uważnie. - This student is careful and listens carefully.

The adjective is uważny. To make an adverb, we usually drop the last letter and add -o or -e. Adjectives ending in -ny almost always take the -e ending. When you add it, the n softens into an ni sound, creating -nie. So uważny (careful/attentive) becomes uważnie (carefully).

What is the exact difference between uważny and uważnie in this sentence?

Uważny is an adjective describing the noun uczeń (student). It changes its ending based on gender and case. Uważnie is an adverb describing the verb słucha (listens). Adverbs never change their form, no matter who or what is doing the action.

Does uważny mean careful like 'watch out for danger' or careful like 'paying close attention'?

In Polish, uważny specifically means 'attentive' or 'paying close attention'. If you want to describe someone who is cautious or careful about danger, you would use a different word: ostrożny.

Why is it Ten uczeń and not To uczeń?