1. I'm thinking that when you installed the 7 cog freewheel you added a washer or something to the right side of your axle. Try to find one the same thickness on the left side and take it out. That'll make your wheel fit more easily in the dropouts.
2. Your wheel is out of dish due to the freewheel change. Redishing is easier than you think. Loosen every left side spoke 1/4 turn and tighten every right side spoke 1/4 turn. If you're careful and accurate about doing that, it won't affect the wheel trueness or anything else. After doing that test fit your wheel in your bike frame and flip it over the other way. When it looks even, you're done.
3. Adjusting the brakes to fit your out-of-dish wheel and spreading the frame to fit a wheel that has been modified to be too wide - those are examples of the tail wagging the dog.