I'm not really familiar with Apple extreme but here's what advice I can give you:
1.) With thick walls almost any router won't be able to do a whole house that is large. Some suggestions: It might not be best to use extreme or any other one without internal antenna. IDK if Apple has a different design but usually routers with antennas outside perform better. Also, if it does have them outside some routers allow you to change them to get different antennas that should work better. Read reviews on Amazon. Some routers can give 300+ feet (which will be much smaller with thick walls but still). (See #2)
2.) A good alternative:
Not sure where all the less than 5 star reviews are coming from. I set
the router up yesterday (and I'm not an IT guru) in 15 minutes.
Secured wireless on both frequencies with different SSID's for each
and unique passwords. Range is at least 50 ft better than the Linksys
e2000 that it's replacing. And I'm getting great speeds throughout my
2 story, 2100 sq. Ft. Home and at least 75 ft. into my back yard.
Entered this review from my iPad 2 while drinking an adult beverage
from my patio. Highly recommend this router to anyone that wants great
range and fast download speeds!
Despite the no antennas (ironically) it seems to have 300mbps wireless and 900mbps over Ethernet. Seems like a nice alternative with fairly good range but you'll have to read through many more reviews with your house to make a wise decision.
3.) That is a common approach... you don't have to use that brand although. They are genericly a powerline adapter. MAKE SURE TO DISABLE DHCP ON SECONDARY ROUTERS IF USING SAME SSID. You may also consider adding routers that are designed to pick up the original WiFi signal and repeat it ("repeaters").