Serving In The Royal Navy And Expanding Skills?

I am VERY excited about joining Her Majesty’s Royal Navy!
Like I said previously, I am going to the RN careers office tomorrow (Tuesday), but there will surely not be enough time to ask all the questions I have!
When I am serving on a vessel, obviously I’ll have my duties. But from what I have read, it seems that (for most staff), wake up call is at 7am, then reporting for duty at 8am. Working until 4pm. (I read this somewhere).
What does one do during your “off time”? I am not joining the Royal Navy to go on holiday. I want to work and serve. Aside from Honour, Loyalty, Courage and Dedication – my personal work ethos has alway been one of being worth more to your employer than what you are paid. I understand the RN will use me to my fullest, but is it possible that provided A)my duties are completed thoroughly and B) my commanding officer approves can I;
1) Go to various parts of the ship and get training on say, weapons systems, see how chefs prepare meals or learn how to do basic engineering? Like I said – I know it isn’t a holiday cruise – but I’d like to know more and be able to do many things if the need arose. (I’m not trying to be a teacher’s pet – I just want to serve with all that I have in me!)
2) Put in some extra shifts for experience?
3) if it is true that a normal duty shift runs from 8-4, what does one do during one’s off time?