An external monitor for my macbook late 2008. Trouble? I use a macbook 13' late 2008. It is perfect for traveling but when I am at home I would like to use an external monitor.

Before buying anything, I have some questions. The monitor I want is:

http://www.lg.com/us/monitors/lg-E2770V-BF-led-monitor

My questions:


Can a macbook 13' late 2008 use a Full HD screen such as that one?
Can I connect the macbook and the monitor using the HDMI port?
I don't want to have the macbook open when I am using the external monitor. Is that possible?
Since the macbook is going to be closed, I would need to connect an external keyboard. Any problem with that?


Thanks

Edit:

Is a macbook 13' late 2008 aluminium unibody
To answer your questions:


Per the MacBook specs, your MacBook shouldn't have a problem pushing video to a 1080p display, as the GPU can support up to 2560x1600 resolution.
You'll want to use the Moshi Mini DisplayPort to HDMI adapter if you want to use HDMI. Note: on your model this will do video only, not audio. This shouldn't make a difference on your display, but I thought you should know. Support for through Mini DisplayPort is added in the Mid 2010 models.
You can accomplish this by using clamshell mode.
As you'll read in the above clamshell mode support article, you actually have to use an external keyboard to get it to work in the first place, so you're good here. You can use a wired or wireless keyboard/mouse for this. 


Hope this helps. Good luck!