Studio flash light

I have recently bought a 180w mini studio flash light, a softbox, an umbrella and some reflectors in order to have a first try in studio photography. My intention is to use the studio set with the following cameras; mamiya c330, mamiya m645 1000s, and with my speed graphic. I realised that the flash manual indicates the time of flash is varying between 1/500 - 1/800s. Could someone help me and explain to me what does that mean ?
As i have understood the mamiya C330 can be used at all speeds.
Am I right ?
My next question whether I can shoot in speeds lower than 1/500 or I am restricted to shoot between 1/500 - 1/800 ?
Thanks

synch options - flash duration

the flash will fire all of its output in 1/500 for full power, and perhaps shorter IE 1/800 at reduced power.

If the camera shutter is fully open for longer than 1/500 then it will see all of the light that the flash emits. If it is a lot longer - like 1/60, and there are other continuous bright sources of light around - IE a window, shooting outdoors, etc, that other light source will also have the chance to influence the image on the film. Usually the light emitted by the flash is quite a bit brighter, so the other light source's contributions are typically quite minimal.

For cameras that do not have in the lens leaf shutters, then the shutter speed selected will have to be slower than its 'synch' speed, the speed at which when both of its focal plan curtains are fully open. Otherwise, if shooting at faster than synch speed, only part of the shutter window will be open to allow light to the film while the flash is being discharged.

Yes, the 330 can be used at any speed. The sync selector must be set to "X" to work properly with electronic flash.
The 645 uses a focal plane shutter & has a sync speed of around 1/60th sec. it's usually indicated in red It can be used at any speed lower than it's sync speed. If you use it at higher speeds you will only expose a portion of the negative. You can see the effect by removing the film cartridge & viewing through the back of the camera and using different shutter speeds.