VAT is paid upon purchase and you shouldn't have to pay any additional VAT or taxes on purchases made from the likes of EuropeanMint, GoldSilver.be, CoinInvest (SilverToGo). VAT will be applied and displayed on the order summary when you make a purchase, if this is applicable. Most of the Silver you buy from the above-mentioned sites will be VAT free (except some items on CoinInvest from my experience. VAT is still payable on non-PM items (capsules, boxes, delivery etc).
1. As mentioned before, you will see what VAT is payable at the time of purchase and you will pay it then (if any). The price question is a bit trickier. Whilst you might get a cheap price at one dealer, the delivery fees are quite steep (silver is heavy and insurance is expensive) and vary from dealer to dealer and depend on country of delivery. You'd have to make a judgment based on how much you plan to buy.
As a tip: always have the display price in Euro for most of the EU dealers - price in £, $ or any other currency might add significant premium to the items when comparing the converted value in Euro.
2. If you order from outside the EU, there will be VAT and possibly import fees (depending on item). Plus shipping would be significantly more expensive I imagine. I would personally stick with EU based dealers at least in the beginning.
3. (alternative) Buy from the forum here. Lots of great deals going on and some sellers will ship internationally. Having a premium membership will help as most good deals are completed within a few hours of listing. Also, come 1st of January 2021 there might be some different rules on shipping.
I bought so far from all the dealers mentioned in the first paragraph. I paid VAT only on accessories (non-precious metals) and some coins on CoinInvest which weren't classed as VAT-free. VAT was paid at the time of purchase.
Payment is another thing to look out for, most dealers will ask for Bank Transfer. Use Revolut or TransferWise to transfer to them with low/zero fees straight in EURO. PayPal is often an option but you'll most likely have to pay the commission (3-4%) which isn't worth it. Same to payments with CC or Crypto.
There's a group order done by @BackyardBullion every now and then which saves on delivery fees, but I wouldn't think it would benefit you so much as delivery to Romania would cost more than UK delivery. Tip: Follow him on YouTube, his channel has some great and well balanced content.
Overall I suggest starting with relatively small amount from one dealer to try it out see how comfortable you are with it and see how the delivery process goes (DHL/UPS which most dealers use will deliver to Romania). Eventually, if you know someone else locally that's interested in buying group up, buy in larger quantities and save on delivery.
Lastly, feel free to browse around the forum, it's full of useful information and there are some raffles now and then where you can win some shiny stuff. Hope this gives you some clarifications, but feel free to PM me if you have any other questions.