परिस्थितियों के अनुकूल ढलना

It's formal, but not 'stiff'. You can use it with colleagues or in serious conversations with friends. For very casual talk, use 'set hona'.

Yes! 'मैं यहाँ की ठंड के अनुकूल ढल गया हूँ' (I have adapted to the cold here) is perfectly natural.

'Badalna' is just a general change. 'Dhalna' implies a purposeful, positive shaping of oneself to fit a specific requirement.

Always 'ke anukul'. Adding 'liye' is redundant and grammatically incorrect in this idiom.

Yes, in a biological context: 'जानवर जंगल की परिस्थितियों के अनुकूल ढल जाते हैं।'

Not necessarily. It usually implies a smart adjustment to survive or succeed, not a moral compromise.

Use 'नहीं ढल पा रहा हूँ' (Main paristitiyon ke anukul nahi dhal pa raha hoon).

Yes, often in emotional scenes where a character talks about their struggle in a new city or life phase.

'लकीर का फ़कीर होना' (to be a slave to tradition/rigid) or 'जड़ होना' (to be rigid).

Yes, to describe how partners adjust to each other's habits.

In this phrase, it functions as an adverbial adjective meaning 'in accordance with'.

Yes, 'Halaat' is the Urdu-origin word for 'Paristiti'. It's very common and slightly more poetic.