I'm making a map where the roach is used to borrow move to scout. However, there are some detector units with a small range (like 3).

Is there a way to make an ability to make the roach undetectable for a period of time? This mean they cannot see it on the map or minimap, they cant see the circle and exclamation mark from a sensor tower, they can't click it, they can't attack it (until the ability wears off).
Or is there a way to do the opposite - temporally take away the detection ability from near by units?

I don't have access to the editor right now, so I can't double check, but I believe detection is a behavior, and behaviors can be removed/toggled with abilities, (much like stimpacks), and possibly even with triggers. If nothing else, you can force an ability use with a trigger.

In the Data Editor, go to your [UNIT]>Unit tab>CUnit_FlagArray> and check e_unitFlagUndetectable.
I'm sure there is some way to flip this flag through triggers and such, but in there you'll find all you should be looking for, like the Undetectable, Unradarable, Unclickable, Un-etc.

There is also an undetectable and not on radar flag for all units.

Talking of units' flags, why do I see "can't select" and "can't move" all around on units that I in fact -can- select and move?

Because it doesn't make any sense once again.