According to Catholicism, what are angels and what are they for? I am a Roman Catholic and believe in angels, so I would like to know more about angels and their characteristics. It would be very useful if answers are related with biblical comparisons. 


What is an angel?
What is their purpose?  
Where they will be?
How many are there? 
What do they look like (a spirit/physical body)?
A thorough answer would occupy volumes as this article shows: Angels | New Advent. The following serves as an introduction

A good summary and introduction is found in the Catechism of the catholic Church 328-336. In part (sans footnotes)


  I. THE ANGELS
  
  The existence of angels - a truth of faith
  
  328 The existence of the spiritual, non-corporeal beings that Sacred Scripture usually calls "angels" is a truth of faith. The
  witness of Scripture is as clear as the unanimity of Tradition.
  
  Who are they?
  
  329 St. Augustine says: "'Angel' is the name of their office, not of their nature. If you seek the name of their nature, it is 'spirit';
  if you seek the name of their office, it is 'angel': from what they
  are, 'spirit', from what they do, 'angel.'" With their whole beings
  the angels are servants and messengers of God. Because they "always
  behold the face of my Father who is in heaven" they are the "mighty
  ones who do his word, hearkening to the voice of his word".
  
  330 As purely spiritual creatures angels have intelligence and will: they are personal and immortal creatures, surpassing in
  perfection all visible creatures, as the splendor of their glory bears
  witness.


This answers but two of your bullet points


Where they will be? I do not understand. Their abode is the heavens but they go wherever God's want them to accomplish his will which is done in heaven.
How many are there?


I quote from the New Advent article


  The number of angels
  
  The number of the angels is frequently stated as prodigious (Daniel
  7:10; Apocalypse 5:11; Psalm 67:18; Matthew 26:53). From the use of
  the word host (sabaoth) as a synonym for the heavenly army it is hard
  to resist the impression that the term "Lord of Hosts" refers to God's
  Supreme command of the angelic multitude (cf. Deuteronomy 33:2; 32:43;
  Septuagint). The Fathers see a reference to the relative numbers of
  men and angels in the parable of the hundred sheep (Luke 15:1-3),
  though this may seem fanciful. The Scholastics, again, following the
  treatise "De Coelesti Hierarchia" of St. Denis, regard the
  preponderance of numbers as a necessary perfection of the angelic host
  (cf. St. Thomas, Summa Theologica I:1:3).