The expression क्यों न is similar to the English expression “why not …” or “Why doesn’t / don’t …”. It is used to make mild exhortations or suggestions that ostensibly have the same form as questions. It generally requires the verb to be in the subjunctive mood.
क्यों न अभी जाएं – “Why not go now?” / “Why don’t we go now?”
जाने से पहले हम क्यों न कुछ खाना खाएं – “Why don’t we eat some food before we go”
क्यों न तुम ऐसा करो कि उसको कल चाबी लाने को पूछो – “Why don’t you just ask him to bring the key tomorrow”
The final sentence could be simplified to “क्यों न तुम उसको कल चाबी लाने को पूछो“. However, for more complex sentences, separating clauses with कि is sometimes useful.
The pronoun is optional, since it is often implied. If a pronoun is used, then it may come before or after क्यों न, but it typically comes after क्यों न, as in the final example.