I ride bents and regular bikes and have used bikes with schrader and presta valves for decades.
1) The tubes in this bike are the Presta tubes. What if I switched to Schrader tubes... does that make sense to do that?
No. First of all, you would have to drill out the rims which would weaken them (definitely a bad idea). Besides, most bike tubes are presta and they have technical advantages
1a) Relating to 1) above, to get a small pump that fits in a bag on the back of the seat, can I find a Schrader pump that small?
I'm sure you could, but the fact that the pumps you're seeing fit presta should help you answer 1). A frame pump might be a better way to go. The Road Morph is the easiest to use because the foot peg gives you leverage and the hose prevents you from accidentally tearing off the stem. It is a large pump though.
2) To avoid punctures, do you recommend a tire liner, or Slime, or something else?
Get good tires. Newbies often get thick tubes or Slime. I've known a lot of cyclists, but I've never known an experienced one that uses slime. It's heavy, it can mess up your pump, and it's only good for certain types of small holes anyway. Tire liners are awkward, especially when you change a tire. Get flat resistant tires -- there are many to choose from. The closest you can get to flat proof is Schwalbe Marathon Plus, but they are heavy.
3) Do you recommend a certain kind of patch kit to have around the house? What about the kit to bring on the tour?
There are tiny patch kits with self adhesive stickers that are easiest to use. I'd get one of them. Bring a couple spare tubes also.
4) Which is better for a recumbent, helmet mirror or handlebar mirror?
Helmet. The take-a-look is best. With a helmet mirror, you can turn your head and look behind at any angle.
5) I've found performancebicycle.com as a website to order bike parts (I live 90 miles from the nearest bike shop). Any other suggested websites to order bike parts, etc.?
For bents,
http://hostelshoppe.com/ is great. Pricepoint.com is a closeout outfit like nashbar and performance, but delivers goods much faster. I've had good experiences with coloradocyclist.com and excelsports.com though they have less stuff that would be good for bents.
But those dang Presta valve stems, man! Previous owner of my bike didn't mention them to me, and one of the Presta stems was missing the knob at the very top. I was able to find someone who knew about these "strange" stems, and he produced a Presta adapter, which worked fine on the other tube. But this one with the missing knob at the top, we tried the Presta adapter on it, and the little post inside the stem is gone, blown down into the tube I'm guessing.
That part was broken off so the tube was ruined before you got the bike -- it would be physically impossible to blow this part down the tube. This would be like someone giving you a schrader tube with a cut stem -- it's not the fault of the design.