#1
What exactly do they do? The power condition seems like a power strip to me basically, so it that basically what it is? and Whats a power attenuator do?

I live in an area where power frequently goes out, so would either of there keep my amp on for a little bit when we lose power to let my tubes cool?
Gear:

Fender Roadhouse Strat
EC-1000 JB/'59
Fender Mark Hoppus bass
Eleven Rack
Peavey Classic 50 power amp
Avatar 2x12
GK Neo 4x10
#2
If you want something to keep your amplifier powered, you need an uninterruptible power supply, or UPS for short. Depending on the capacity you want, there are some that start at around $50 on Amazon.
#3
Power conditioners are basically uber surge protectors, yes. They don't really help you if you lose power. However, if your voltage is not sufficient or varies, it will help stabilize it. Certain power conditioners will also improve your sound by filtering electrical noise. The main purpose is if you're jamming in some ****ty practice spot or venue and there is a surge of voltage, your amp won't blow up.

Power attenuators work kind of like biasing - they suck up some of the power from the amplifier and dissipate it in heat so that you can run your 120 W tube amp in its sweet spot without ear bleeding.
My band - DEADIRON
Playstyle - Rock / Metal / Hardcore / Punk
Main Gear
Schecter Hellraiser C-1
Morley Bad Horsie Wah
Memory Man Deluxe
ISP Decimator

Mesa Single Rectifier Rect-o-Verb
#4
A power conditioner basically makes up for bad wiring. If you live in an old house or apartment, or you regularly play bars, you should think about getting one. I didn't notice a difference in sound quality, but there's a lot less static and hiss, which is a big deal when I try to record. It's especially useful if you have several things on the same circuit ... and note that not every wall socket is its own circuit. If all you have on the circuit is a solid-state amp and a laptop, then you're probably not going to see much improvement. If you have a tube amp, stereo, and a television, then it's going to be a biggere difference.

But again, it doesn't improve - it just fixes.

A power attenuator (or power soak) goes between an amp and the speaker to increase resistance. It's used to get that 'cranked amp' sound at lower volumes. It's about as useful as a 'half power' switch like on some of the new boutique tube amps. If you try to drop the signal further, it starts to sound pretty bad.