Listed or unlisted / addl portfolio / company background

I am a qualified Company Secretary having put over 4 years experience in a listed company in Secretarial Department. For better career prospects, should I look for a job in listed company only. If I move on to unlisted company will it help me to better my career.

Whenever I attend an interview, employer request me to shoulder additional portfolios like Legal / Accounts / Finance / Service Tax. I don't have any practical experience in these areas. How to handle these areas without prior experience?

I am on the look out for job change.  How to verify whether the company’s operations / operations are carried out in ethical manner.