I did a small job for an American subsidiary of a translation agency I use to work for. They ased me to calculate my invoice in Euros and then convert it to USD.
Did they mention any specific instruction as to when conversion from euro to US dollars should take place?
What can I do now?
(How) can I make sure that the clients takes over the costs for the money transfer?
The only thing you could do is ask them, but since you forgot to agree on this, one could argue that the costs incurred at your end are your problem. As an alternative, you're showing a PayPal logo on your profile - why don't you ask them to pay via this route?
And: what exchange rate am I supposed to use?
In the absence of any specific agreement, I would tend to use the middle market rate at the invoice date.