I don't think the description for 'Expelliarmus' is accurate. In the fourth book, during the third task of the Tri-Wizard Tournament, Harry uses Expelliarmus on a giant spider that is holding him up in the air, making it drop him. The spider was not another wizard, but it worked. So Expelliarmus is not only used to disarm another wizard.
I also tried "relashio" for "cuts or rips objects."
On a side note, I'm surprised "nox" isn't on there. It is the countercurse for the light spell. (Not saying what it is, 'cause that's a spoiler.)
The medical name for a nosebleed is 'epistaxis' from the ancient Greek.