1) No, you wouldn't. These errors only come up:
- When you explicitly empty the caches and W3 TC for any reason (usually just because somebody uses the website ;P ) needs to regenerate the cached content. Since W3 TC won't cache the WP admin, you could use WP for days without noticing any error. By default it takes a random, not logged in user to use the site to cause the full cache-ing.
2) For an updated tutorial about how to find the button you need and how to use the whole stuff, please refer to this thread of mine: Illustrated tutorial on how to fix many plug ins that W3 TC breaks
3) About memcached: the defaults listed in those boxes are good enough to get you started so I did not include them in the screenshot.
You just need an IP address (usually either 127.0.0.1 or your host's IP) given to you by your hosting company and a port number. That too has to be given to you by your hosting company.
Basically, you just slam those two numbers in the way shown in the screenshot and you are done with the memcached configuration.
Notice that some tutorials will tell you to also use memcached for other stuff. Don't. Some functionalities are best served by APC, others by simple "Enhanced disk cache".
If you optimize your website well and use APC + memcache (and possibly Varnish) you should get at least B rating both on Page Speed and YSLow.
A CDN is not a bad idea either, I have got good results both with Cloudflare / MaxCDN and self hosted CDN on a domain I created for it.