Speaking from experience if you have a Mac at your school, there is most likely an application monitor which has a white list, and if your application isn't white listed it is not allowed to run. Then by policy all applications must run from /Applications, and limited users (how you authenticate) only has ---r-x--r permissions. Basically you can only read and execute from the /Applications directory.
So, it is most likely going to be very hard to run a portable version of fire fox so you can by pass your school's web filter.
If you figure out how to do it, I am sure there is a job waiting for you somewhere, or your network administrator is not up to snuff with properly policy application, or there is the x factor. X factor meaning, that sometimes you have to implement something a certain way to get it to work and you are forced to deal with the ill side effects.
Also to read/write to NTFS you need to download and install ntfs.progs or FUSE (google search them) and I am certain you will not be allowed to install that.
If I were you, I would just deal with it, because there is most likely not any way around it.
Also, and just for the record, almost over half of the apps out for OS X are self contained, so they can run off of any volume, external device or whatever. I have an external HD for work that holds an OS, several imaging and utility apps, and I run all the applications straight off the external HD. So, you don't need the "portable version" but they are generally smaller in size, so more ideal for thumb drives.