I am in my 50s, new to bicycling, and decided to take up bicycling to stay in shape and stay fit.

I recently bought a vintage (late 70's-early 80's) Centurion LeMans road bike. I am a woman, and it is a bit too high for me, probably a 56-62cm. I would fit comfortable in a 52cm.

I want to convert it to a 'fixie', or single speed bike.

What I want to know is, if I put slightly smaller tires on it, would it lower the height of the bike? Also, to convert it to a single speed, could I still keep one of the brakes?

Basically, would I just remove the gears, then purchase a new chain?

Thank you in advance for your help.