Two questions...

1. Do you get the bonuses from your base armor and clothes when you're wearing it under power armor? For example if your basic armor piece gives you a VATS bonus, does it still apply in power armor?
2. Do power armor piece attributes stack? For example, if I have one "optimized" power arm, should I craft another, or is it redundant?

Thanks in advance!

When you enter power armour, its stats replace those of your personal armour. You can test it out by looking at your PipBoy stats after getting in.

The one exception is the helmet. You can choose to swap between the armour's helmet and your own headgear (or even no headgear) while wearing your power armour, in which case your head will become visible, you'll have the stats of whatever headgear you're wearing, and your character will speak normally instead of using that annoying 'intercom' voice.

Shoot - guess I had three questions: do "normal" armor attributes stack? For example, does wearing two pieces of +10% movement speed = +20% movement speed?

I noticed a definite speed boost when I equipped a second Sprinter leg armour. Not sure if the same applies to power armour, but it should.