The whole note (semibreve) is always four quarter notes (crotchets). This does not change based on the time signature. I can only imagine the confusion if it did!
The term 'whole note' only makes sense in 4/4, or other similar time signatures (common time, 2/2, etc). In these time signatures, the note does take up a whole bar. In other time signatures, it might not take up the entire bar (like 4/2 or 12/8), or it might not fit at all (2/4, 3/4, 6/8). The British naming system system (semibreve/minim/crotchet/quaver/etc) does avoid this issue, in exchange for ridiculous names like hemidemisemiquaver.
My original answer used the term 'beat' as you did in your question, but that seems to be confusing the issue. In 4/4, a beat is pretty much the same as a crotchet. This isn't the case in other time signatures, like 12/8 and 2/2. However, I don't think you're actually intending to talk about such cases. To be clear, a whole note is always four crotchets, but a beat is not always the same as a crotchet. Beat requires a time signature, and to a lesser extent, a tempo (you could argue that a fast 6/8 has two beats, and a slow one has six, with different emphases).
An exception to the rule is the whole note rest. It can be used as a whole bar rest in pretty much any time signature, except in ones where that might be ambiguous, like 4/2. All the other rests and notes always have the same 'duration', regardless of time signature. By 'duration', I mean the ratios of note lengths, as stated in your question. The actual duration (in seconds) of the note will obviously depend on tempo.