In general, you can ignore the currency that an index fund uses internally for reporting. You can buy A1JX52 using USD in the US or using EUR in the EU; the same as you can buy JPY using USD or EUR, whatever is more convenient for you.
I don't know how the situation in general with Banks in Europe. But in Germany you will find many Banks which are convenient and offer cheap access to the stock market. Yes, they will try to sell you shit, but if you select an online bank and know what you are doing, you will never have to talk to anyone and get really good products.
Taxation varies across Europe. Some countries take less than the US, some take more. But pretty much all countries of the western world have double-taxation agreements, so there is no double taxation. A German citizen, e.g., pays not more than 15% tax on the dividend of a US stock. It looks that this is even less than US citizens, but I'm not sure. That is of course and bit annoying when filling out tax forms, but if you invest in an fund, the issuer of the fund does it for you.