I can answer your second question the most clearly by answering the first.  They are not separate from Christ.  They are the "Christ within us", that our faith "activates", (I can't really think of another term.).

The Church officially puts it this way...

(CCC)  "They are infused by God into the souls of the faithful to make them capable of acting as his children and of meriting eternal life. They are the pledge of the presence and action of the Holy Spirit in the faculties of the human being."

Oh no prob.  I'm just trying to explain as best I can.  "Merit" does not mean "earn through works", but it does mean that we must 'cooperate' with our own salvation.  It means we must be faithful to God's will through charity.  I think that may be where Protestants get it wrong about Catholics and "works."  The questions to ask to understand what this means and how it is different from Protestantism is to ask 1.  Who are the faithful?  The faithful are those who freely commits his self to God, by which we believe in God and believe all that he has said and revealed to us.
2. Do we earn the merits for salvation by works?   Our works get their merit only from Jesus' sacrifice on our behalf. We can do "works" 24 hours a day, 7 days a week, 365 days a year for the rest of our lives, but without Christ's grace, they are nothing. Works have no merit in themselves -- and faith without works is not enough. We are saved by grace alone, by faith that works in charity.

Protestants would agree with point #1, but the problem is that their forensic model, (Calvin was a lawyer, already a strike agin' him in my book.  ), is that point #2 does not equate well with that same model.

Lol, Catholics have always believed in a model of TULIP, as we think that Calvin was the most intellectually honest and correct in his statements of theology.  (We have the biggest problem with the "P", however). This sometimes surprises Protestants who accuse Catholics of "Armenianism" or "semi-Pelagianism", while forgetting of course that Pelagius was suppressed and banished and went into obscurity, while Augustine, his nemesis, is venerated by the Church as a "Doctor" of the Faith.  I don't want you to think I am copping out, but there is a link I can give you that is as close as you will find on the Catholic opinion of TULIP...

http://www.ewtn.com/library/ANSWERS/TULIP.htm

Jimmy gets it about as right as any Catholic can.

I personally see Calvinism as a theological groups interpretation of Scripture in which certain texts of Scripture are over-emphasized at the expense of under-emphasizing certain other Scriptures. I find the same to hold true in all other "isms" as well.