I was thinking whether reinstall a new 32bit os and unity or not?
You can use a Windows 64bit OS version, such as Windows 7 64bit, you don't have to install a 32bit OS; simply, if you use Unity 5, you'll need to download and install the 32-bit version of the Unity 5 Editor; that will work on your 64bit Windows OS.
Can the webcam work on unity;s play mode?
Yes
I was thinking whether reinstall a new 32bit os and unity or not?
You can use a Windows 64bit OS version, such as Windows 7 64bit, you don't have to install a 32bit OS; simply, if you use Unity 5, you'll need to download and install the 32-bit version of the Unity 5 Editor; that will work on your 64bit Windows OS.