You should always be cautious of doctrines when presented to you by others and examine it yourself. This is a good rule of thumb regardless of what theological view point one holds.
Indeed. Most Calvinists will tell you that Christ's sacrifice was not sufficient -- nor should it have been -- for the "whole world" but only for the elect. However, neither Calvin nor the Council of Dort ever affirmed that view. Both, in fact, state that the atoning work of Christ should be understood in judicial terms and it had a double intent. That is to say, Christ died with a purpose concerning the provision of his atoning work and a purpose concerning the application of that work. The first represents the universal sufficiency of Christ’s atoning work, and the second represents the effective application of that work in the salvation of the elect. In this view, the atonement is conceived in judicial (rather than pecuniary -- or atonement, ransom, etc.) terms. Jesus died to make perfect satisfaction for all human sin. bearing the curse of the law and of the Father’s wrath against sinners, so that God can justly vindicate all to whom the benefits of Christ’s death are then applied.
John Calvin drew his inspiration for outlining his concept from the Council of Dort, and his students later created the five points. Contrary to popular belief, Calvin did not write those points, and probably wouldn't completely agree with them. They were formulated by his students after his death, and their hyper-enthusiasm tended to make them misrepresent what their mentor taught.