Regarding the question posed, "What is the collective name in English for the sharps and flats you find in the key signature", the answer is "Accidentals", despite comments to the contrary, which I think stem from a fundamental misunderstanding of what an accidental sign means.
An accidental sign does not, as has been mooted by others, mean a note different from those given in the key signature. Rather they mean a note different from one of the notes in the C major/A minor scale, so any sharps or flats in a key signature tell you what notes to play in that key signature that are different to the notes in the C Major/A minor scale/key signature.
Let me explain.
One of the first things you are told in music theory about our standard 12 note western music system is that it is all based on the C Major scale.
A key that's not C is indicated by showing where the notes differ from the C major scale in the key signature. Let's say we are in G Major. G Major has 1 sharp indicated in the key signature. The sharps and flats in the key signature are basically saying, "every time you see this natural note written in the score, play the sharp or flat note as indicated in the key signature instead".
The key signature is therefore just a system of not having to write the accidental note in the score every time it appears in the music. Put another way, if you didn't put the sharp in the key signature, and left it empty, you could simply write each F# explicitly. The key signature would look like C Major but would sound like G Major, (assuming you wrote the music using the Major harmony of G Major).
Indeed, the fact that every key signature can indicate one of two keys, the Major version and its relative minor, demonstrates that all the key signature is doing is telling us which natural notes from the C Major, (or A minor), scale to sharpen of flatten when we see them written in the score.
Look at it this way: Your conductor gives you a piece of music. It has no sharps or flats in the key signature, or in the score, but the conductor says, "Play this, but every time you see an F, play the sharp accidental of F, F#."
If there's another sharp written in the score, say D#, that is indeed a sharp outside the G Major key, but it's not actually telling you to play the sharp note because it's outside the G major scale, but because it's the sharp note above D natural in the C Major scale.
Hence a sharp or flat in the music always indicates a variation in the notes from the C Major/A minor scale, whether it's in the key signature or in the score, and they are all therefore collectively called accidentals.
One last point, you don't talk about a natural sign in a score as being an accidental outside of the home key signature, because it's saying, "ignore the instruction in the key signature to play the indicated note as an accidental, but play the natural note this time, (for just this pitch and this bar...).
This all flows logically from that fundamental concept, that everything in the western system of music is based off the C Major/A minor scale.
And yes, accidentals is a pretty poor label for what it's supposed to mean, and it might have been less confusing if we called them 'intermediate' notes, as they are always half-way between two natural notes, but it is what it is, and we are stuck with it.