All of these options are acceptable, but the first and second ones are probably the best. In some cases, like the one in your last example, an action doesn't happen at one specific time, but naturally and slowly grows over a somewhat longer period of time. You don't really start dating someone at one specific moment: it is a process, not an event.
I would certainly change your sentence to "at that time".
What I believe you are missing is that "in" implies a duration and the phrase is actually a shortened version of "within" and skipping "amount of":
[with]in that [amount of] time I managed to undo the knot.
This means:
- I was given some amount of time
- I was able to complete the task
A longer version of the sentence, to put it in context, would be something like:
I was tied up in a closet and knew the bomb would go off in two minutes. In that time I managed to undo the knot, get out of the closet and escape the building just before it exploded.
And, if you were telling the story to someone, you might include "at that time":
A: Where were you yesterday evening?
B: I was tied up in a closet at that time and a bomb was going to go off in two minutes.
Best Answer
The usage of these three expressions overlaps. Your three examples are all valid and idiomatic. The choice depends on context and preference.
It's not time to ..... is an expression saying that the the person/s being addressed need to be aware their focus is misdirected; under the circumstances they should be thinking of something different.
It's no time to..... makes the same point but more strongly - with more emphasis.
It's not the time.... could have been used in either or both of the examples above. Once again it makes the point that the person/s being addressed are not focusing on the real issue. They need to turn their attention elsewhere.
Much of the time you could use any of the three expressions. Only the nuances vary from one to another. It's not a question of right and wrong but rather of context and choice.