Windows 7 - long/short and upper/lower filename

I am using Windows 7 64 bits.

1)

I have a filename called ze_xmlfun.prg Last week gitgui shows 2 changed files: ZE_XML~1.PRG and ze_xmlfun.prg At momment I can't update this file, because get a error. Try delete file, update one name each time, but same error. Seems that a unique file is considered as 2 files, and this causes error.

2)

When do a search in history, upper/lower case must be the same as in git control. If upper/lower is changed, is considered a new file. How to configure git to work allways using lower case on Windows?

3)

Is there a plugin or a tool to make this, to new files and to update in git repository?

Note: gitgui is a gui tool for git, ok, but once it uses git, may be 
this feature/change need to be made in git.

José M. C. Quintas