1) Your bike is fine. Lots of people tour on hardtail mountain bikes with racks.
3) I second the recommendations for thinner slick tires (tyres!!). If you'll be on roads most of the time, they'll be faster, roll better, and be just as comfortable.
4) Here's a link to a pretty well-reviewed, inexpensive tent. It goes for about $100 on Amazon in the US.
4b) Yep, just lock it up. Sometimes I'll tie one of my tent or hammock lines to it for added security. If someone moves it, I should notice it.
5) I don't think a drop bar conversion will be necessary or effective (plus you'll also have to spring for new shifters and brake levers). Bar ends and locking ergo grips will give you enough hand positions.
6 & 14) I've done plenty of touring in regular shorts with padded undershorts on a Brooks saddle. I know Brooks saddles aren't for everyone, and they're expensive, but I love my B17. I also recently bought a couple pair of these undershorts. Very comfy so far. Just make sure that your outer shorts don't have baggy pockets or thick seams in places that will rub between your legs/butt and the saddle. Casual shorts of a thinner material work well, and you don't have to bring on type of shorts for on the bike, and another for when you're off the bike.
9) I don't know much about hand crank chargers, but the ones I've seen have been garbage. The new Shimano dynamo hubs are great, and not that expensive. You can power the lights on your bike and charge your phone while riding.

Check out crazyguyonabike.com. Heaps of good touring information there. Sounds like it's going to be an awesome trip! I look forward to hearing more about it.