The short duration of your initial contract makes this a bit more complicated. If you are leaving for at least one full tax year, you can fill out the P85 and you will get the tax rebate quickly because you declare that you will not earn any more income in the UK before 5 April 2017. If you aren’t sure that is the case, then you can’t claim the rebate yet. But you still need to fill out the form.
Have a look at PJM1964’s link and if you are unsure, you can call the tax office or pop in to one of their ‘shops’.
You can pay towards NI up to 6 years after the missing qualifying years. I agree it is a good idea.
Edited to add: This is the link to determining your residency status – UK tax residency. As I said, the short contract muddies things somewhat and you may find you pay tax twice and have to claim rebates in both the UK and India at the end of their respective tax years.