Learn Italian: Che pena! Il topo è morto. - How sad! The mouse has died.

Even though che pena expresses an emotion, che here is an exclamation meaning 'what a' or 'how', not the conjunction 'that' connecting two clauses. Because there isn't a main verb expressing emotion followed by a dependent clause (like mi dispiace che...), the subjunctive isn't triggered. The second sentence is just stating a fact.

Does 'pena' usually mean 'pain' or 'penalty'? How does it mean 'sad' here?

While pena can mean 'penalty' (like in pena di morte, death penalty), in everyday language it often expresses pity, sorrow, or compassion. The exclamation Che pena! is a very common way to say 'What a pity!' or 'How sad!'.

Why is there no article between 'Che' and 'pena'? In English we say 'What a pity'.

In Italian, exclamations starting with Che directly attach to the noun or adjective without an indefinite article. So 'What a pity!' is simply Che pena! and 'What a beautiful day!' is Che bella giornata!.

Is 'è morto' the past tense ('has died') or is it the verb to be with an adjective ('is dead')?

It works as both! Morto is the past participle of the verb morire (to die), which takes essere to form the past tense, meaning 'has died'. But morto is also an adjective meaning 'dead'. Both interpretations make perfect sense here and are grammatically identical in Italian.