Why do leaders in the Roman Catholic Church wear red garments? I understand that the color red can mean a variety of things (Holy Spirit, Pentecost, presence of God, blood of martyrs, etc.), but what specific meaning(s) does the Catholic church place on this color of garment, and who is permitted and/or required to wear red, and under what circumstances?
Cardinals wear red because it symbolises blood, that they are ready to shed their blood in defence of the faith. It's also why the Pope's "official" footwear is red: that symbolises that he is ready to walk the way of the martyrs which is stained with the blood they shed.
From now on, they devote even more to work with me in governing the universal Church, and to be witness to the Gospel to the point of sacrificing their own life. This is the meaning of the red color in their clothes.
Red dress is reserved for cardinals, although red is used to a lesser extent for lesser dignitaries. In particular, chaplains within the papal household can wear cassocks with red piping and buttons, which denotes their affiliation to the Pope.
Vestment Color Indicating Liturgical Season
With respect to vestment color, the appropriate document for the Catholic Church is the General Instruction of the Roman Missal, which has quite a long section on the color of vestments as part of Chapter VI, "The Requisites For The Celebration Of Mass".
With respect to colors of vestments in general, paragraph 345 states:
Diversity of color in the sacred vestments has as its purpose to give more effective expression even outwardly whether to the specific character of the mysteries of faith to be celebrated or to a sense of Christian life’s passage through the course of the liturgical year.
As far as wearing red in particular, paragraph 346 gives us:
As regards the color of sacred vestments, traditional usage should be observed, namely:
b. The color red is used on Palm Sunday of the Lord’s Passion and on Friday of Holy Week (Good Friday), on Pentecost Sunday, on celebrations of the Lord’s Passion, on the “birthday” feast days of Apostles and Evangelists, and on celebrations of Martyr Saints.
I can't find what I consider an authoritative description (clearly attributable to Church hierarchy or to official Church teaching) of why red is chosen for those days specifically, although (as you point out) red can indicate the presence of the Holy Spirit through fire (as on Pentecost), or can indicate blood (as in the celebration of Good Friday or of the feasts of martyrs).
The mere fact that red can or could be used to indicate other things does not mean that it is in fact used to mean those things in the Catholic Church, and certainly not that the use of red is thereby any less appropriate.
Cardinals Wearing Red Vestments
I did find a reference in a story from EWTN, which cites a formula the Pope uses when he gives a new cardinal their red biretta (their hat):
The Pope places the biretta on the cardinal's head and pronounces a formula which includes the following words: "(This is) red as a sign of the dignity of the office of a cardinal, signifying that you are ready to act with fortitude, even to the point of spilling your blood for the increase of the Christian faith, for peace and harmony among the people of God, for freedom and the spread of the Holy Roman Catholic Church".
Again, then, we're back to red as a representation of the (potential, at least hypothetical) spilling of (one's own) blood for the Church.
This is part of the new rite for the creation of cardinals, which was promulgated by Pope John Paul II in 1991. It is reasonable, however, to believe that this interpretation of the color symbolism dates back considerably further than that time - indeed it appears that the word cardinal with the meaning of "a particular shade of bright red", and indeed the name of the bird called "the cardinal", is due to the red vestments used by the cardinals.