No you can't. It's the same as 'Good Morning' in English - you don't answer 'the same to you' for nobody's wishing you anything :( The words we use to wish a nice day are 'Miłego dnia' = 'Have a nice day'. That's when you can respond 'Wzajemnie'.

You should respond also with "dzień dobry". You can also use for example "Witam" when you are a host or "cześć" when you meet a younger person or a friend. We use "wzajemnie" or "nawzajem" in response to someone's wishes, on Christmas, birthday etc. It means "the same to you". For example: - Życzę Ci powodzenia na egzaminie. - "I wish you luck on the exam" - Wzajemnie. - this means that we also wish the first person good luck on the exam. or: - Wesołych świąt! - Wzajemnie.

If you other person said you "Dzień dobry", you always answer " Dzień dobry" sporadic use answer "witam". These greetings are very official.

No, yo must say "dzień dobry"