Sorry about the delay in getting back to you.
My (initial) cart bug was caused by the native currency selector (+Shopify Multicurrency + Shopify currency app). After uninstalling all of this and installing a third-party currency app, most of the bugs have disappeared.
However, I've just identified another cart bug when you a) change currency, b) remove item from the cart, c) add new items to cart - you are then unable to proceed to proceed to checkout. The bug "stays" with the user until they switch the currency to default (EURO) and try again so it indicates that Shopify has some bugs to fix related to they Multicurrency checkout feature.
My recommendation would be to hire a freelance Shopify developer to investigate the issue as I would not have identified/solved the problems myself.
Hope it helps @David28 - Happy to hear you've fixed your bug @aliceshops. Would be great to get some input from the Shopify team as well.