Unforseen Bicycle?

I went out to a bar called The Pig and Whistle today with a friend from club. It's described as a British pub, so I had hopes their fish and chips would be decent. They were actually pretty good. My chicken and chips was pretty good as well, and the dressing on the salad was the perfect amount, which I thought was pretty cool. We ended up spending about two hours there, and had some pretty good conversation.
I'm getting in the habit of using a lot of diagrams. I drew, to scale, the US, four different cartridges (.22LR, .223, 12G, and .45), and made an attempt at Portugal. And between my friend and I, we sketched out a unit circle and poked fun of my math.
By the way: KMD, you make for a great topic. I've talked for hours about my crazy American friend with twenty guns and a box of assorted knify bits.

Anyway, the bike, which is the subject.

[Edit: I seem to have forgotten to mention that a new bike, from a bike shop, will cost between $120 and $200. Probably towards the upper part of that range, since I want a bike with more than one gear.]
[A second edit: I should also mention that while Kyoto has a very usable mass transit system, it's small enough that I can get anywhere on my bike just about as fast, and while getting exercise, and it's free. I was just doing some math, and if I go downtown once a week for the remaining time I'm here - and I am much more likely to go two to three times a week - it would end up at about $120, assuming I never use the buses, which are much more expensive. This is why the "walk, you bum!" option isn't really.]

As it would turn out, my bicycle's rear brake chose today to decide that it would get stuck half engaged. Today, I went 6 miles (8.4km) - not a long way, right? - with the rear brake half engaged.
I thought I was just being particularly out of shape at first, and then it started to squeak more and I realized what the problem was. I tried poking at it, but this is Japan, so I can't carry my Leatherman with me. I kicked it a couple of times for good measure, and generally pried at it with my flashlight, but to no avail.

I poked at it anyway on a couple of different occasions. On the way back, it was extra sludgy, though not as squeaky, so I did my best to go at a decent speed in spite of it. I stopped at one point in hopes of getting a picture of some policemen, but they said they can't do that while they're working. When I got back on, I felt the brake assembly, and it was a touch under 100 Fahrenheit after two to three minutes of cooling in humid air.

I'm going to try and disconnect the brake so I can use my bike tomorrow morning, but I think I'm going to see about buying a new bike either this weekend or tomorrow afternoon. What I'm thinking is that this bike cost me about $60 with the registration and whatnot. Having the tires replaced would cost about $30, and that needs to be done anyway, 'cause they only hold a safe amount of air for about three days. After that, the tires slide sideways on slight slopes. So, $30 there.
I have no idea how much it would cost to have the rear brake fixed, but I can't identify anything wrong with it, and I can't imagine it will cost any less than having the tires replaced. So, figure another $20-30 for that. We're up to at least $50.

The light on my bike won't engage when the tires are wet, which is exactly the kind of situation where I want cars and other cyclists to know I'm there. Those are about $15, plus an unknown installation fee, though I could probably do that myself. About $65, so we've now exceeded the original purchase cost of my bike.
To add to this, there are no reflectors on the wheels, and only a small one on the back and just the light on the front, so I'm nearly invisible at night. Good situation, right?

Then we can get into things that aren't actually broken, but are merely inconvenient. This is my first bike of this sort, so I'm looking at it much like my FZ8: a learning experience to grow from.

• Height: It's a small bike, even for a Japanese person, which I am not. The seat does not go nearly high enough to make for a proper ride.
• Gears: This bike has one gear: "Go." Seriously, it has just one gear. This is fine as long as you want to go roughly ten miles an hour and never encounter a slope, but it's not so great if you're trying to not get run down by cars doing 30km/h.
• Racks: The basket on this bike is small, and it's rounded, so a lot of things just don't fit into it. Oh, and the paint burnt off where someone tossed a cigarette into it, for some reason, so it's going t
  The back rack is the same as just about every other one, though, so no complaints there
• Form: If I wore an ankle-length skirt, this would be a great bike in terms of form. But I don't. I wear pants. And the traditional triangle shape is traditional for a reason: it's strong. The wobbly curves of this bike are scary if you put any more than about twenty pounds on the two racks.
• Even when the rear brake does engage properly, it still doesn't effectively slow me down, it more just makes a loud squawk and tells people that I'm there. This has it's uses, but I'd prefer that it didn't do that. I'll be avoiding a rear drum brake if possible.
  

I will totally take the pedals off, though, and have them put them on the new bike, when and if I do buy a new one. That should only cost about $5, and then I get to keep my $20 pedal investment. As it is, this bike has too many things wrong with it for me to feel safe riding it, let alone comfortable. But these are things I would never have considered before I bought it, and now maybe some of you will have been able to learn from this, as well. Most of this has been bother me for a while, but the whole brake thing makes it effectively unridable. I can walk next to it with less effort and at the same speed.
I'll make sure to post a picture once it's gone, if I can't fix it, since I haven't put a picture of it up as yet.

[eloquent segue]

Like I said, I'm looking at this bike as a learning experience; it cost me, but now I know much more clearly what I do and do not want in a bicycle. Hopefully I can sell it back to a cycle shop for $20 or something, and they can fix it in-house and resell it at the same $50 price or something.

Input would be appreciated.