I must remember to bath within ten minutes time.
Is the word "time" needed in this sentence, or is it superficial? Is it even wrong to remove it?
There are only two quantities 'minute' describes -
It is clear from the context of the sentence that you're not talking about angles so 'time' is superfluous in this sentence. It may not be incorrect, but it certainly isn't 'native speaker' usage.
It sounds wrong with "time" to me but I can't come up with evidence my feeling is correct. "In ten minutes time" is definitely correct and "Within ten minutes" is definitely correct.
No, you shouldn't use "time" in this context.
You do something "within" a period of time, but "ten minutes time" denotes a single point in time.
The expression is ten minutes' time (i.e., the time consumed by ten minutes), not ten minutes time. It's generally acceptable, but it's a bit idiomatic and I don't think adding the possessive plus "time" is ever strictly necessary.