My Bike doesn't seem to fit itself I have a project bike. I made it myself from bits recycled.   It is currently a single speed, although I'm thinking of adding gears to turn it into a bit of a commuter/excercise bike. 

Before I do that, I really need to sort out the fit.  It doesn't seem to fit me, or even itself very well.

Bike dimensions - 51cm seattube, 50cm top tube, chain stay 41cm.   tires are 700x32.  

The problems:


The bike has a seat tube length of 51cm which seems right for me at 5'6.  When i sit on it my leg is straight at the bottom of the stroke, However there is virtually no standover room.  
the bike seems pretty cramped horizontally, that is the handlebars seem too close to the seat.  in fact i'm not sure if the top tube is long enough. 
The front wheel, despite being the right size to line up with the brake, seems to be way to close to the downtube, and as a result clips my toes sometimes when I'm pedaling. Does this bike even fit itself?
both wheels are pretty tight through the brake.  That's probably because of the chunky tires. 


What have I done wrong? How can i get the bike to feel a bit less cramped?
The geometry of this frame looks odd. 622mm wheels are too large to fit comfortably in a 51cm frame. Usually sizes this small are made to compensate with very steep seat tube angle to let the rear wheel forward and very shallow steering angle to avoid toes clipping front wheel. This bike has been made the other way around and that is why it looks and feels strange.


With saddle as low as shown in picture, the frame is too high for you. With horizontal top tube, there should usually be about hand's width of seatpost showing. The saddle should be roughly horizontal.
Longer handlebar stem or less swept back handlebars will help.
This is a problem with all small frames with large wheels. Is the fork the original one? Some older bikes came with steep steering angles and very high fork offsets. The offset eliminates some of the problem with toe overlap but makes steering twitchy at high speeds.
32mm tires are the absolute maximum size to fit inside short reach brakes. Normally the kind of brake is used with 23mm to 25mm tires.


Edit: @Will's comment led me to the idea that this bike could have been a 650B or at least converted into one. That would reduce the standover height and allow wider tires and also explain the strange-looking angles. Smaller wheels would lower the bottom bracket, so saddle would still look too low.