This doesn't happen to me.
Are you sure it isn't just the fan in the power brick? I have something that sounds like a fan in mine when it gets hot.
There is no fan in the MagSafe power supply.
I didn't know that. Do you know what causes a whirring sound in the MagSafe 95Watt power brick that came with my MacBook Pro 17"?
Should be 85W, but anyway... If you're putting your ear up to it, you might be hearing some component vibration due to the input a/c frequency (buzzing at 120Hz).
Will unplugging every time I shut down and plugging back in after I turn it on like 10 hours later affect the health of the battery in any way?
Doubtful it would ever be noticed, if it even did. But, if you're keeping the charger itself plugged in, you aren't saving any power off the mains by disconnecting it from the MBP anyway - small amount that it is. As I mentioned, there really isn't any significant power used if it is connected.
This is a fairly new MBP so the battery health was still at 100% for the past month but in the last 2 days it dropped to 99% for some reason... and I've been trying the unplugging-plugging in thing for the last 2 days... could this be the reason?