As an ARMY Reservist is it possible for me to go to any military schooling such as Pathfinder school or Paratrooper?

Yes it is. But here is the catch. With the tightening of the money getting schools like that are going to be difficult UNLESS you are sitting in a position in your unit that authorizes the ASI(Additional Skills Indentifer) example: My current duty position has an ASI of F7 (Pathfinder) that means I should at some point attempt to get Pathfinder qaulified.

Be leary though. Ive been seeing and hearing alot of scuttlebutt about "come on over to the Reserve/National Guard side of the house we can get you all of the Hooah schools" That is not necessarily the case. They are using these tactics (Recruiters) to lure Soldiers over to get their numbers up.

SGT (Join to see) Yes you can, I went to Airborne while in Guard and Air Assault while in the Army Reserve. You need to find a unit that has this mission and they will fund the school.
Bottom line the unit must have the mission for you to get the school, then you need to compete to get the slot.

There are lots of great Army schools you don't get an 'I love me' badge to hang on the uniform. You need to focus on the why you want these skills and how it will be used.
SFC (Join to see) Gave you great advice, which is why Senior Officers listen to Senior NCOs, you should do the same!

It depends on your command and funding. I'm a company Training NCO in the USAR so I TRY to put soldiers on school all the time. Since I arrived at my current duty location in September I've only been able to send 3 soldiers to get MOSQ. We've had quotas for Mountaineering, Air Assault, Airborne, ABIC, etc. I've submitted so many and they've all been denied due to funding. I'm not trying to kill your dreams but right now funding for schools is very low. MOSQ and NCOES are the priority. Hopefully next FY there'll be more money for the fun stuff.