Yes, they have many martial applications. Most of them go beyond the self defense mentality, and fall into the 'martial' mentality.
The harmonizing effects are a byproduct of correct practice.
And scotty is correct. You have to find a good teacher who shows you the applications. Many times, what you see from the outsider's point of view is just a tiny part of a whole picture. For example, in Xingyi's Pi Quan, you see it and you could say "Hey, that's a palm to the head". but that's only 5% of what Pi Quan could really be.
Scotty...good one about the Taiji punches
"I'm into murders and executions, mostly"