I work p/time and still don't pay any NI as I don't earn enough. It's not a problem as long as your Child Benefit is in your name. Whoever recieves it gets NI contributions paid for them by the government, as they assume you're at home with the kids. There is a passage about it in the handbook you get, I'm sure there must be something online too.
It's called HRP - Home Responsibilities Protection - I think some carers get it too.
I have had my max no of years (child benefit for 22 years and counting!) and they send me letters occasionally telling me how much to pay to make up the rest - you can pay retrospectively for 5 or 6 years, and if it's a year where you worked a bit and paid some contributions you can make it up to a full year by paying the difference.
I'm not entirely sure tbh, although I really should shouldn't I
I don't pay tax as I earn just under my limit which is roughly £4500pa. I do sometimes pay a little bit of NI because of the weird way I get paid. I get paid the last friday of each calendar month so sometimes I have 5 week months and if I've done a couple of extra hours I'll lose a bit to NI, but I think in the whole of the last tax year I paid the grand total of £6.61!
It doesn't matter if you earn under the threshold because your NI/pension/whatever will be credited with whatever minimum amount is required.
God knows about personal pensions - I haven't got one either! (DH has but hardly puts anything in it - he is still contracted out of SERPS, I keep telling him to get back in (he is nearly 53) but he never gets around to it. Will have to stand over him.)
Ring the 0845 number on that pdf link I gave you, np. Last time I had a letter about this I rang them and got a lovely bloke who explained it all in words of one syllable and a gorgeous Geordie accent