Learn Farsi: آن تخت سفته، ولی این صندلی نرمه. - That bed is firm, but this chair is soft.

This is the colloquial Tehrani shortcut for است (is). Since سفت (seft) and نرم (narm) both end in a consonant, the spoken 'is' becomes a short '-e' sound attached to the end of the word. So, سفته (seft-e) means 'is firm' and نرمه (narm-e) means 'is soft'.

How would this sentence be written in formal Farsi?

In formal Farsi, the full verb است (ast) remains a separate word. The sentence would be written as آن تخت سفت است، ولی این صندلی نرم است.

Is the letter ه at the end of سفته and نرمه pronounced as an 'h'?

No, the 'h' sound is completely silent here. When the letter ـه or ه acts as the reduced verb 'is' after a consonant, it only represents the short vowel '-e'.

I have also learned سخت for 'hard'. Why is سفت used here instead?

سفت (seft) is specifically used for physical firmness, tightness, or rigidity, like a firm bed or a tight knot. سخت (sakht) is mostly used for abstract difficulty, like a hard exam or a tough situation.