If you are in full-time education you will be exempted from Council Tax (a letter from your FTO is usually sufficient), but I doubt you will be eligible for any state benefits - that was a dodge the government put an end to many years ago.
As for NI, you can make a payment to address any shortfalls during the time you are training and this will restore your full NI credits for any state pension - assuming you believe this will still exist when you need it. The Tax Office will usually write to you at some point to enquire why no NI payments have been received for X period of time and to invite you to make up the shortfall. Isn't that nice of them?
