As for Euro in Czech Republic, it can get a bit messy.

In most frequent tourist destinations, there is no problem in paying in Euro or via card, with exception of small shops or stalls. However, there's another caveat. The shops often have their own exchange rate which can be rather skewed-usually it's somewhere in range of 20-24 CZK / 1E, while actual exchange rate is fluctuating in 25-28 CZK range. Also, they might accept only Euro notes, not coins, and give you change only in CZK. It's also worth keeping some Czech change at hand, for some small spur of the moment purchases at stalls and transportation-public transport, which usually deals in small prices (24 hour pass for public transport in Prague costs 110 CZK, less than 5 EUR, to give you some idea) usually accepts only CZK, and the ticket machines in most cities accept only Czech coins.

So whenever you're paying with Euro here, it's worth asking about these details beforehand and if something seems really shady, ask for a receipt if they did not give it to you. According to law, if you paid with Euro, the exchange rate must be on receipt, as well as any surcharge by seller (not bank if you're using card) related to it, and it's your right by law to recieve a receipt.