This gives the STEEM seven days to regenerate its power
Got it. Since voting power regenerates at a linear rate of 20% per day, even completely tapped Power will be 100% regenerated in 5 days (less than 7). Hence by powering down, your Steem Power is bound to loose at least 2 days worth of voting influence.
Yes, but you gain it if you power up (or get delegation).
Delegation is something I didn't mention but the same thing. If someone delegates you 100,000 SP and you are low on VP, you will get the full voting power of that new delegation and it will not be crippled by your current voting power. When you lose it though, you lose that power as well.