Learn Italian: Non ho ancora comprato questo quadro raro da regalare. - I haven't yet bought this rare painting to give as a gift.

When an infinitive verb tells you the purpose or intended use of the noun right before it (like quadro), you connect them with da. So un quadro da regalare means 'a painting to be gifted'. If you used per here, it would imply the painting itself is doing the gifting!

Why is ancora placed right in the middle of ho comprato?

In Italian, common adverbs of time like ancora (yet/still), già (already), and mai (never) usually squeeze right between the two parts of the passato prossimo. Here, it sits exactly between the helping verb (ho) and the past participle (comprato).

Could I use the verb dare instead of regalare?

While dare is the general verb for 'to give', regalare specifically means 'to give as a gift' or 'to present'. Since the English translation says 'to give as a gift', regalare is the perfect word to use here.

Why is it questo quadro raro and not questo raro quadro?

Demonstrative words like questo (this) always go before the noun, just like in English. But descriptive adjectives like raro (rare) almost always come after the noun they describe in Italian.