I am a professional conference interpreter, so I guess I can say something about the OP’s query. First, I am not a translator, I am an interpreter. Translators have time and dictionaries, they strive for accuracy, perfection even. We must be humbler: we strive to convey the gist. There are goob and mediocre interpreters, of course: the better ones get more details across, the bad ones give us a bad name, and everything in between. You also have good and bad days, good and bad speakers, and subjects you know more or not so much about. Professional interpreters try to inform themselves about as many details as possible before the meetings, of course.
There are several modes of interpretation, roughly: simultaneous (in the booth, with microphones, usually in a team of two or even three per language), consecutive (with a notepad, often for formal occasions, often just one per language, sometimes one interpreter does both ways, what we call a retour) and sussotage (whispering interpretation, where an interpreter sits close to a small audience and whispers in simultaneous mode.)
Most interpreters work only into their mother tongue (what we call the A language) from one or more other languages (what we call B or C languages. B languages are perhaps not mother tongue, but close, and some work into their B languages under certain conditions, eg only in consecutive. We do ot work into C languages).
Very few people are truly bilingual, it is not even a clear consensus about what that means. I, for instance, was raised bilingual Spanish/German, went to school in Spain and to university in Germany. My linguistic skills in Spanish and German are very good, but different in both languages. For instance, when I do arithmetic in my head I usually do it in Spanish, as this is the language in which I learned to multiply.
An interpreter cannot ask the speaker to repeat or to slow down (much as we would sometimes like to!): in the booth it is technically impossible (the speaker does not listen to your channel, but to the other, and not at all while speaking), in formal settings it is highly undesired. If you don’t get something, that is too bad. Interpreters must be able to be humble. Misunderstandings happen also in monolingual conversations, deal with it. If the listener has a question, it is up to him to ask.
This assumption could not be more wrong. An interpreter’s hell could be a South American politician being flowery to be translated into sober German. It could also be an elder Japanese speaker speaking English.
The most difficult thing for many interpreters are numbers. As we try to convey meaning we visualize things, but numbers are just numbers and have no meaning beyond the number. When in a booth a good colleague writes the numbers down for the colleague doing the interpreting: reading a number is easy.
It is difficult enough to get the numbers right without the conversion, but I try to. It is my way of showing off in front of my colleagues. The customers do not usually notice.
So, my meeting starts now. I have to go! Do not hesitate to ask more details if you are interested.
Ah, yes! I almost forgot: this the website of the International Organisation of Conference Interpreters
aiic.net
We are happy to assist and will try to answer any query you might have.