UPDATE!
Today I took my bike on the route I wanted it for; to my local train station and back again. The first part of the journey is about 5 mins on road, then 14 minutes on flat rubble before coming back to the road for the final 1 min.
Firstly, the front brake works perfectly. I was worried about it being too tight (like aidanpringle pointed out), but the brake pipe didn't work it's way out of the callipers once. I've since added a rear brake (all the parts came through the post yesterday) since I was also concerned about flipping over the handlebars, or my first problem (that the front brake pipe would work it's way out of the callipers). If this happened at least i'd still have one brake!
I've also raised the seat about an inch and pumped the tyres up a lot. This made a huge difference, since I was so fast today when the path was clear ahead of me. A smaller change is that i've added longer handlebar grips. When I removed the front and rear derailleurs, I naturally removed the gear cables and shifters. This left a big gap on my handle bars that my previous handlebar grips couldn't fill. This is more of a cosmetic change than anything else.
One of the odd things about this bike, which give it it's weird shape, is that i've since noticed the frame is too small for me. The bike came with a long saddle stem, so I kept putting that up and ended up hunched over the old handlebars. The new handlebars, ridiculously long as they may be, actually fit me perfectly. I haven't noticed any lack of precision when turning, or reverberations when I hit a big bit of rubble which I think is what you're meant to experience. The handlebars are exactly where i'd like them to be.
Overall, i've got my bike the way I want it. I might buy a rear luggage rack so I can go to the shops for my mum, or some road tyres if I find my commute path changing. If I get really bored, I might remove all the stickers from the frame. I like the silver colour of the frame, and the words plastered all over it detract from that.
P.S: A big thanks to all the people who have helped me with my problems. I've got a bit of a cycling bug right now, so I might post a few more queries over the coming weeks. For now, bye!