1) Please specify the time and date you want your order to be ready. ( Does it sound correct in written english?)
2) Please specify when you want the order to be ready. ( Does it sound correct in written english?)
3) My supervisor told me to get the order ready according to/at the specified time. (Should I use according to or at?).
Don't put a space after an opening bracket.
#1 and #2 sound OK.
With #3, "according to" definitely doesn't work. You can use "at the specified time" but the sentence is ambiguous. Does the "specified time" refer to the time the order needs to be ready or the time your supervisor spoke to you?
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.