As to the questions:
As others have said, you don't pay NI on earnings until you earn £110 per week. If you are paying NI at the moment you are getting a tremendous hourly rate for part time work.
You are required to register as self employed with the Revenue by three months after you began trading at the latest. You can do this yourself by contacting them directly or an accountant will handle things for you. Up to you, depends how much it's worth to you to avoid the hassle.
You don't have to pay any NI on your self employed earnings unless you are making a fair bit from it. NI is paid based on earnings per "job". However you will likely have to pay tax unless combined earnings from all taxable sources are less than your personal allowances. You'll have to do a tax return. Tax returns must be completed by 31st January for the year ended 5th April in the previous year. So if you were trading before 5th April 10 you will need to do one imminently. If not then there's no panic at all but that doesn't get you off the hook for letting the Revenue know within three months that you are actually trading.