"Catholic" is like the opposite of a word such as Jacuzzi, Xerox, or Kleenex. The latter are brands that have become synonymous with a specific meaning: hot tub, copy machine, tissue. The former had a specific meaning, and is now associated with a "brand" of Christianity. The former meaning is that you can think of the word "Catholic" as a synonym for the word "Universal". That should clear up the first item in your question: there is one universal church of Christ. Don't let all the denominations fool you: depending on which group you subscribe to, the meaning here is either that they are all part of the Lord's church, or not really Christians at all (though this latter view is rare). Stating belief in this church in the creed is stating your full acceptance of all that the Church teaches1.
In talking about "communion of Saints", the creed is not referring only to those who have been granted the formal title, such as Saint Augustine or Saint Paul. It refers to everyone who is sanctified by the blood of Jesus... in other words, all Christians. When the creed says that they are in communion, it reminds us that we are all followers of Jesus: not Calvin, not Luther, not the Pope, but Jesus, and reminds us of his prayer in John 17 that "they may all be one." It also refers to a connection we all have to Jesus, through the Holy Spirit.
1Side note to the answer, but within the context of a denomination, this often refers specifically to the teachings of that said denomination, and sometime even for the denomination to assert authority over it's supplicants. This is one reason why the denomination I belong to does not support the use of any creed. We believe it's up to the individual to study and find out for themselves what God's word says, and a big part of formal church worship time is to help and support you along that road.