If I am to apply at a telescope for viewing objects, how to determine (easily) what is the minimum and maximum possible RA and DEC visible from that telescope during that time of the year. For eg, take the telescope at paranal (24.6258°S, 70.4310°W) and if I observe anytime from October to March.
In the Southern hemisphere, the maximum declination you can see is 90-L where L is your latitude. The minimum is -90, since you can see the south celestial pole.
As the earth rotates and revolves, you can see any right ascension within those declinations.
The only exception is that you ordinarily can't see stars that are too close to the Sun. However, the Sun moves enough between October and March that all right ascensions will be visible at night sometime between October and March.