1) Ground school is 2-3 weeks. OJT is anywhere from 2-3 months or more depending on how comfortable you are working the desk. Remember that these are international wide bodies and Kalitta flies them over every continent (except Antarctica), so it's a lot to process especially if you're coming from a few years dispatching 30-40 min hops at a regional. As has been said before though, the training has improved dramatically over the last year.
2) Yes, you don't get jumpseat privileges until sign-off and finger printing, but it does incentivize you to get signed-off faster!
3) They have agreements with most major airlines and regionals. There's a full list somewhere and an unofficial Jumpseat Guide PDF once you get signed off, but I've never had a problem jumpseating with any carrier that didn't involve an ornery gate agent.
4) Yes? I'll be honest, I've never been in one of their planes besides the 747 cockpit sim (which is awesome), so I can't answer that with certainty, but I would assume so. Ironically, jumpseat privileges don't require FAM rides on each plane type you dispatch (Kalitta is still Supplemental, and thus legally Flight Followers, not Dispatchers), so I can't comment on what any of the flight decks look like. However, I've heard rumors that FAM flights will be written into the union contract at some point. Whether that will be this union contract or not remains to be seen.
5) You're welcome.