There is a lot you can do in 45 minutes. Take a look at the beginner's routines sticky in the main forum and look for "simplefit." It's a routine of pushups, pullups, and squats. You don't need weights, just a place to do pullups, and it's plenty challenging for someone starting out. You won't get big on it, it's not that kind of routine, but you'll get stronger and get stamina as well.
Heck, here it is:
Read their diet suggestions, too. The guy who runs it basically endorses "The Zone" by Barry Sears, but it's good eating advice to keep in mind even if you don't eat that way.
You diet will need more work than that. Bananas are good, but you'll want more fruit than that, and more varied fruits - oranges, apples, pears, whatever else you can get. Mix it up. Same with vegetables. Get lots and get varied - try to eat a good mix of green leafy veggies (spinach, romaine lettuce, etc) and cruciferous veggies (broccoli, cauliflower, etc.).
Eggs are fine. Hard-boiled eggs are just handy. Eat the whole thing, don't toss the yolk, it's the fattiest portion but it's also where all the nutrients are. Don't be afraid of fats.
The raisin bran is okay, but where is the protein? That's all carbohydrates (bran, raisins). Add a few nuts (almonds and walnuts aren't expensive and are good sources of nutrients) and some protein - dried meat is good for that, so is whey protein power. Bring some dry whey powder and a shaker cup and you can mix it up on the spot. Cans of tuna in water are also good, although I doubt it'll taste so great with the raisin bran.
Whenever you eat, try to get some protein, some carbohydrates, and some healthy fats (omega-3 fatty acids, mono- and polyunsatured fats, it's easy to get saturated fats). Check that website I referred you and look at their "healthy foods" list.
You should also read through ALL of the stickies on this forum. It's good stuff, and the admins have done a good job of sticking stuff up there everyone could benefit from reading. You've got to do your homework to really benefit from these forums, but you'll learn a LOT about eating properly in the process.
Hope that helps,