Yes they do battle. Remember when Daniel was praying for 21 days and the messenger Angel was delayed by the Prince of Persia? Michael had to come and help him so he could pass and get to Daniel.
There are many types of Angels. Some appear as men, they have different jobs to do. My understanding is that we each have two Angels assigned to us, one is a scribe Angel that writes down all of our thoughts, words and deeds, and the other is a guardian Angel. I heard a sermon from a pastor which said something along the lines of...the Armor of God which we put on, is also what is provided to our Angel or something like that. So it is important for us to think cooperatively and be cooperative with our own Angels. (I wish I could remember exactly where I heard that).
Remember when Elijah went up in a whirlwind? I heard a testimony from a certain Pastor (Bruce Allen) who said the whirlwind was not just a whirlwind, but an Angel which piloted the chariot which took Elijah up, so there's another type of Angel...