Does everyone have to play in the same key or is the key accustomed to the instrument section? for example, clarinet would use Bb major?
Yes, and no! Everyone sounds like they're playing in the same key, yes, but looking at the actual music in front of the players, no.
There are lots of transposing instruments about, which don't, for many reasons (answered here for several questions) see the music in the same key as non-transposing instruments. An example would be the Bb clarinet, which actually plays a tone LOWER than the written music. So, music for that clarinet needs to be written in a key a tone HIGHER, to compensate.
Horns, likewise, play notes which they may call certain letters, but the sound produced is actually different letters (note names). So, their music needs to be written in keys which transpose what they read into what's actually needed to be in tune with everyone else.
If you look at the score - the music the conductor references - you'll see that even for a passage where everyone is playing in unison, each instrument will have the music written out in the key which makes it sound unison.
This is more of a comment really but I don't have the rep to post it as such.
Whilst I mostly agree with what Tim has said it occurs to me that there is no reason for this to be always true. There are piano pieces where the left hand part and right hand part have different key signatures (e.g. Prokofiev's Sarcasms 3rd mvt), so I would not be surprised if there are orchestral pieces also.
A quick Google search gave this page in Wikipedia - https://en.wikipedia.org/wiki/Polytonality - which cites a number of examples going back to the Baroque period.
The Bb Flat clarinet is a transposing instrument of a whole tone down. Simply put when the clarinet plays a C note what you actually are hearing is a Bb.
So technically the Bb flat clarinet will be notated in a different key than the non-transposing instruments but when you relate it back to concert pitch then it all comes back to the same key.
To add to Neil's comment, given that when the clarinet player plays a C, it sounds like a B-flat, then to compensate, you must tell the clarinet player to play a D so that it sounds like a C - and thus matches the C played by the rest of the orchestra.
If you're writing a piece and are looking to arrange it for band or orchestra, I highly recommend tracking down a copy of the book "Essential Dictionary of Orchestration" by Dave Black and Tom Gerou. You might be able to find a copy at your local library. That's how I found out about it - by stumbling across it at the library (and then I later found a copy at a used bookstore for about three dollars).
Another cool book is "Principles of Orchestration" by Nikolai Rimsky-Korsakov. Rimsky-Korsakov was a famous Russian composer and arranger from time period of the late 19th to early 20th century. So it's cool to see a famous composer talk about how to arrange songs, although you'll probably find Black & Gerou's book to be more useful than Rimsky-Korsakov's.