1. No cost to register for VAT
2. Depends on the service used. If courier this will be door to door. Courier will make Customs Entry without reference to you if low value (£18 or under) as a simplified entry and no tax will be collected by HMRC. If you are a business, they should conact you to obtain your VAT no. for the entry and check if you have your own Deferement Approval Number to pay taxes due.
Couriers get away with a lot that the conventional airfreight community can't. Not that I'm bitter !
It generally comes down to how export invoice has been done. You will see many Hong Kong ebay sellers selling goods for peanuts and making their profit on the shipping. If their sales invoice only shows the sale value, and it is under £18, it will be part of a bulk clearance and very unlikely to arouse the interest of HMRC.
If goods arrive traditional airfreight into LHR and, you will get a call from a freight company at the airport advising you of arrival. What you pay for from them depends largely on the shipping terms (Incoterm) agreed with seller.
This will range from just Duty/VAT/Fee for paying taxes to all the charges from departure to delivery. You could come to LHR and collect or let the freight agent arrange for you. This will be cheaper as they will have vehicles/subcontractors covering UK wide deliveries.
Good luck.