Firstly VAT - You can register voluntarily for VAT if you wish, if you are under the current threshold (nearly £80K turnover). If your business will turn over more than this you MUST be registered. However, if your customers are individuals, this makes all your sales 20% more expensive than an unregistered competitor, so the usual advice is that voluntary registration to sell to domestic customers is unlikely to be good for you. You will pay 20% to HMRC on your stock, but that's on the trade price, not the retail price.
So if you buy £100 worth of stock, the supplier will charge you £20 VAT if you are registered, you recover £20 VAT from the Government, however, if you sell this stock for £200, you will charge your customer £40 VAT, making the real cost to the customer £240, and pass the £40 on to HMRC. If you are not registered, you can't claim the VAT back, but you can keep everything you sell it for - so if you keep the price at £240, you make a bit more.
The VAT and import duty, if applicable, is charged by the freight company (TNT, FEDEX, UPS etc) and a handling charge for them paying it on your behalf.
The supplier fills in a declaration of the value (which they often under price) - this is what the duty and VAT are based on. Invoice wise, you just need documentation to keep the tax people happy - same as normal.
There's no problem with any laws. Importing gets really expensive when you have weight and size - apart from that it can be fairly cheap. I've had a quick look at the CE Marking list, and I can't find hair extensions listed there, so CE marking seems not to be required. You'll probably NOT have to pay duty - I couldn't find a category for extensions, but most hair products seem to not attract duty.
So expect VAT on your supplies (usually 2-3 weeks after it is delivered), no import duty, and this VAT won't be recoverable, but you won't need to pass on any VAT on sales while your turnover is low - which will save you money.