In Canada parallel runways spaced closer than 2500 feet can't be used simultaneously for takeoff and landing operations.
Yes they can. YYZ south parallel complex (06L/24R and 06R/24L) is 1000' centreline to centreline. In VFR weather they are used independently. In IFR weather they are dependent.
The north parallel (05/23) is about 2 miles from the south complex and they are used independently but there are rules in place to permit simultaneous, parallel arrivals and departures in all weather conditions, even low vis..