Most of the question asked here are answered in the DWP booklet "Your State Pension Explained", Google DWP042, and download it as a .pdf from the .gov site.
You can get a State Pension Statement by crayoning in the form BR19, or search for "State Pension Statement". This gives you the date you will reach state pension age,qualifying years,weekly pension amount & amount deducted if you were contracted out, (COPE).
You can also check your National Insurance Record by filling in the online form at the .gov site, search for NIStatement. This will show you any gaps in your record, what your qualifying years are, any years you can pay for, what it will cost & the date you have to pay by.
You get 1/35th of the full state pension for every year that you pay, at present this works out at £4.45 per week per year paid.