Validation on atleast one image and others can be video or images on same file uploader.

may be something like this?

public function rules()
{
    if($this->image){
        return [
            'image'   => 'your validation',
            'video'   => 'required',
        ];
    }
    else if($this->video){
        return [
            'video'   => 'your validation'
            'image'   => 'required',
        ];
    }
    else if($this->image && $this->video){
        return [
            'video'   => 'your validation'
            'image'   => 'your validation',
        ];
    }
    else{
        return [
            'video'   => 'required'
            'image'   => 'required',
        ];
    }
}

not tested, hope you get some idea :)

Access file properties. See this http://www.angularpluslaravel.com/how-to-save-uploaded-file-in-the-server-in-laravel-2/