Sourcing or making smooth edged glass tiles
I agree with Elmy's comment about glass being a bad choice for this application.  But if you are intent on using it, here are some ideas.

Microscope slides are roughly the width you want and can be cut to length.  A skilled glass cutter (say someone who makes windows or works with stained or leaded glass), can quickly cut strips and pieces from a sheet.
Glass corners and edges can be ground smooth by doing it under water.  You can even cut glass microscope slides to length with a scissors this way; snip them submerged in a basin of water.
You can melt glass in a microwave kiln.  Microwave kilns are relatively inexpensive to buy or even make yourself, and can melt glass and metals in a home microwave oven.  Melted glass jewelry is commonly made in these.