Well, still nothing fixes my gamepad behaviour, so i post some details here, too.

Model: Saitek P580 (PC-USB / Dual Analog / RumbleForce)

lsusb parts for my gamepad:
Bus 001 Device 004: ID 0f30:0111 Jess Technology Co., Ltd 

lshal-parts for my gamepad:
udi = '/org/freedesktop/Hal/devices/usb_device_f30_111_noserial'
  info.linux.driver = 'usb'  (string)
  info.parent = '/org/freedesktop/Hal/devices/usb_device_1d6b_1_0000_00_04_0'  (string)
  info.product = 'Colour Rumble Pad'  (string)
  info.subsystem = 'usb_device'  (string)
  info.udi = '/org/freedesktop/Hal/devices/usb_device_f30_111_noserial'  (string)
  info.vendor = 'Jess Technology Co., Ltd'  (string)
  linux.device_file = '/dev/bus/usb/001/004'  (string)
  linux.hotplug_type = 2  (0x2)  (int)
  linux.subsystem = 'usb'  (string)
  linux.sysfs_path = '/sys/devices/pci0000:00/0000:00:04.0/usb1/1-1'  (string)
  usb_device.bus_number = 1  (0x1)  (int)
  usb_device.can_wake_up = false  (bool)
  usb_device.device_class = 0  (0x0)  (int)
  usb_device.device_protocol = 0  (0x0)  (int)
  usb_device.device_revision_bcd = 257  (0x101)  (int)
  usb_device.device_subclass = 0  (0x0)  (int)
  usb_device.is_self_powered = false  (bool)
  usb_device.linux.device_number = 4  (0x4)  (int)
  usb_device.linux.sysfs_path = '/sys/devices/pci0000:00/0000:00:04.0/usb1/1-1'  (string)
  usb_device.max_power = 200  (0xc8)  (int)
  usb_device.num_configurations = 1  (0x1)  (int)
  usb_device.num_ports = 0  (0x0)  (int)
  usb_device.product = 'Colour Rumble Pad'  (string)
  usb_device.product_id = 273  (0x111)  (int)
  usb_device.speed = 1.5 (1.5) (double)
  usb_device.vendor = 'Jess Technology Co., Ltd'  (string)
  usb_device.vendor_id = 3888  (0xf30)  (int)
  usb_device.version = 1.1 (1.1) (double)

udi = '/org/freedesktop/Hal/devices/usb_device_f30_111_noserial_if0'
  info.linux.driver = 'usbhid'  (string)
  info.parent = '/org/freedesktop/Hal/devices/usb_device_f30_111_noserial'  (string)
  info.product = 'USB HID Interface'  (string)
  info.subsystem = 'usb'  (string)
  info.udi = '/org/freedesktop/Hal/devices/usb_device_f30_111_noserial_if0'  (string)
  linux.hotplug_type = 2  (0x2)  (int)
  linux.subsystem = 'usb'  (string)
  linux.sysfs_path = '/sys/devices/pci0000:00/0000:00:04.0/usb1/1-1/1-1:1.0'  (string)
  usb.bus_number = 1  (0x1)  (int)
  usb.can_wake_up = false  (bool)
  usb.device_class = 0  (0x0)  (int)
  usb.device_protocol = 0  (0x0)  (int)
  usb.device_revision_bcd = 257  (0x101)  (int)
  usb.device_subclass = 0  (0x0)  (int)
  usb.interface.class = 3  (0x3)  (int)
  usb.interface.number = 0  (0x0)  (int)
  usb.interface.protocol = 0  (0x0)  (int)
  usb.interface.subclass = 0  (0x0)  (int)
  usb.is_self_powered = false  (bool)
  usb.linux.device_number = 4  (0x4)  (int)
  usb.linux.sysfs_path = '/sys/devices/pci0000:00/0000:00:04.0/usb1/1-1/1-1:1.0'  (string)
  usb.max_power = 200  (0xc8)  (int)
  usb.num_configurations = 1  (0x1)  (int)
  usb.num_ports = 0  (0x0)  (int)
  usb.product = 'USB HID Interface'  (string)
  usb.product_id = 273  (0x111)  (int)
  usb.speed = 1.5 (1.5) (double)
  usb.vendor = 'Jess Technology Co., Ltd'  (string)
  usb.vendor_id = 3888  (0xf30)  (int)
  usb.version = 1.1 (1.1) (double)

udi = '/org/freedesktop/Hal/devices/usb_device_f30_111_noserial_if0_logicaldev_input'
  info.capabilities = {'input', 'input.mouse'} (string list)
  info.category = 'input'  (string)
  info.parent = '/org/freedesktop/Hal/devices/usb_device_f30_111_noserial_if0'  (string)
  info.product = 'Jess Tech Colour Rumble Pad'  (string)
  info.subsystem = 'input'  (string)
  info.udi = '/org/freedesktop/Hal/devices/usb_device_f30_111_noserial_if0_logicaldev_input'  (string)
  input.device = '/dev/input/event9'  (string)
  input.originating_device = '/org/freedesktop/Hal/devices/usb_device_f30_111_noserial_if0'  (string)
  input.product = 'Jess Tech Colour Rumble Pad'  (string)
  input.x11_driver = 'evdev'  (string)
  linux.device_file = '/dev/input/event9'  (string)
  linux.hotplug_type = 2  (0x2)  (int)
  linux.subsystem = 'input'  (string)
  linux.sysfs_path = '/sys/devices/pci0000:00/0000:00:04.0/usb1/1-1/1-1:1.0/input/input9/event9'  (string)

Xorg.0.log-parts for my gamepad:
(II) config/hal: Adding input device Jess Tech Colour Rumble Pad
(**) Jess Tech Colour Rumble Pad: always reports core events
(**) Jess Tech Colour Rumble Pad: Device: "/dev/input/event9"
(II) Jess Tech Colour Rumble Pad: Found x and y absolute axes
(II) Jess Tech Colour Rumble Pad: Found 1 mouse buttons
(II) Jess Tech Colour Rumble Pad: Configuring as mouse
(II) XINPUT: Adding extended input device "Jess Tech Colour Rumble Pad" (type: MOUSE)
(**) Jess Tech Colour Rumble Pad: YAxisMapping: buttons 4 and 5
(**) Jess Tech Colour Rumble Pad: EmulateWheelButton: 4, EmulateWheelInertia: 10, EmulateWheelTimeout: 200
(WW) Jess Tech Colour Rumble Pad: unable to handle keycode 291
(WW) Jess Tech Colour Rumble Pad: unable to handle keycode 290
(WW) Jess Tech Colour Rumble Pad: unable to handle keycode 288
(WW) Jess Tech Colour Rumble Pad: unable to handle keycode 294
(WW) Jess Tech Colour Rumble Pad: unable to handle keycode 295
(WW) Jess Tech Colour Rumble Pad: unable to handle keycode 298
(WW) Jess Tech Colour Rumble Pad: unable to handle keycode 289

I really have no problem with my gamepad controlling the mouse, that would be ok at least, if the mouse position from the d-pad or analog would NOT be absolute, so i can really move the mouse with the gamepad and it not jumping back to center position AND if the gamepad would at minimum work in games ;-). I hope this sum up is no spam :D