How many kind of manual flash making vivitar company slr camera

You may be better off posting to cameras instead of the camera flashes category.

NO!
Do not use this flash on your camera without something like this to protect the camera.

Follow the instructions on page 2 of the manual. If you don't have a manual, you can download one from http://butkus.org/chinon/vivitar.htm

Pretty much any flashgun with a standard hotshoe. The 3800N is extremely basic and does not take advantage of any dedicated flash functions, so you'll find loads of cheap or even free basic manual or auto-exposure flashguns on auction websites and also on FreeCycle.

I'd suggest a basic manual flashgun as you then fully control it. Automatic flashguns try to second guess what it is you're photographing so can often over-expose the subject. You also learn more using a basic manual flash which is probably the only reason to buy a 3800N in the first place.

Most probably find a Vivitar Vivicam repair manual here. Just send them a search request.

Freestyle Photo $1.00 each

Vivitar went out of market some years ago. If you need product manuals there are several site in the web.

Find a user manual for download here:
http://manualfox.com/link/vivitar.htm

You can download a PDF version at http://www.butkus.org/chinon/vivitar.htm

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The shutter on these cameras is complete manual, so the batteries don't enter into its operation. If the shutter button isn't doing anything (be sure you operated the winding lever to cock the shutter!), then it probably means there is a mechanical problem that will require professional intervention. These cameras are very inexpensive (about $140 new, with lens), so it may cost more to fix it than to just buy another one. They have decent lenses and usually are pretty good cameras. They are made by Cosina, a Japanese company that makes cameras for a number of "name brand" companies.