As has been indicated, the £2.50 charge is for using a credit (rather than debit card). It apples both online and at Post Offices. (For several years, credt cards couldn't be used at Post Offices to pay for Road Tax. If you tried to use one you were asked for an alternative means of payment and/or advised to take out a cash advance on your credit card, which in itself incurred charges from the lender. Writen from experience!):
https://www.taxdisc.direct.gov.uk/EvlPortalApp/app/home/help#topic2
Getting the tax disc away from the surrounding paper is easy if you keep the forefinger and thumb of one hand (either side of the paper) touching those of the other hand while keeping the perforations in the middle. Not that it matters much anyway because, as has been written above, the tax disc will shortly disappear. Further, you'll be able to pay monthly (as well as 6-monthly or annually) by direct debit:
https://www.gov.uk/government/news/direct-debit-and-abolition-of-the-tax-disc