Can i charge if Macbook is switch off?

Hi,

The reason i am asking this question is because i am experience unusual behavior.

As you know, there is no more indication aside from MBP 2010 with the LED, or MagSafe with the LED.

Issue:

Charge Macbook with the lid open, upon seeing charge bar appear, i cover the lid.

An hour later, i stop charging because i have an appointment with friends which i have to leave home. Stop charging afraid the Macbook will overcharge.

Came home continue charging for 2 hours, stop charging after 2 hours, did not switch on Macbook to check whether the power is 100% charged.

On the following day, when i switch on the Macbook, it was only 8% power.

Questions:

Should the Macbook charge with just the lid open?

Should the Macbook charge with power on + lid open?

Can the Macbook charge with lid close without powering on the Macbook?

In fact, i have experience twice during charging, without powering on the Macbook with the lid close, it is not charging at all.

Any solution on charging notification?

** I wish Apple can develop an application that work in-conjunction with iPhone, whenever the Macbook is fully charge, the iPhone will send an notification informing to stop charging, however, my feeling is the Macbook has to be power up, in order to synchronize the notification with iPhone.

If iMessage can send an notification to iPhone, it will be a fantastic.