A Specialist is an E-4, which while technically is the equivalent of corporal, is not the same in authority. The specialist ranks came into being to keep paper pushers from getting bossy with line troopers (or so it's told). Specialist used to go all the way up to E-8 IIRC, but it's not important because all the rest were thrown out years ago. The Specialist E-4 is the last vestige of this.
A Corporal, on the other hand, is the lowest ranked *true* NCO. They are expected to be troop pushers, and generally get all the drawbacks of being an NCO and few of the perks. Since it's usually a place keeper promotion, it's something to be endured
If you get to a line unit, what you'll find is that E-4's who have not yet attended PLDC and are not yet promotable (through lack of points or time in grade) will be Specialists, and there will be many of them.
On the rare occasion where it's needed because of troop shortage neccessitating an NCO in a slot or outstanding acheivement from the soldier in question, the E-4 may receive a lateral promotion to corporal. Typically it's a sign of trust from the chain of command to do this.
Speaking from personal experience, the 12B MOS was so critically understrength in lower EM's, but so full in E5+, that you'd rarely see a specialist get promoted except maybe twice a year when the zone scores dropped. So, there'd typically be a corporal or two in the company before they were promoted to SGT E5.
Second, your recruiter is full of crap. If you can go into the military, you can go to jump school, you just have to volunteer. The youngest person in your class gets dubbed "keeper of the wings" and their job is to always have a set of jump wings on them (provided), clean them, polish them, and make them look pretty. It's something of an honor, and if the keeper zero's out, it's a bad omen. Usually never happens.
Third, if you can't figure out how to exit the aircraft correctly, god help you. I've seen guys jumping mortar baseplates, Dragon missle jump packs, M60s+radios, etc. It's pretty hard to screw it up unless you are negligent, especially with "walk out the door" which is what we were using in 91-4. If you are completely ate up, you might manage to route your static line incorrectly, get it caught on a riser assembly or catch your equipment on the door (though I can't see how), but those things are few and far between.
Ranger Justin is more up to speed with the current standards, he can fill you in more.
Finally, Andy, 33 years old qualifies you to be in the special Geritol section of basic... ya old bastid!
Kevin