That's for PowerShell, not DOS. IIRC, for DOS you could do something like "dir /s *.txt" to list all files with .txt extension in all subdirectories of the current directory, so "dir /s x" would be somewhat equivalent to Unix's "find -name x" (not as fast as "locate x", but should return the same if run on the root directory, and if there were no changes since the locate database was last rebuilt).
I've used that before and the functionality isn't even close. The UNIX command is fast, while the recursive PS command takes forever and prints tons of garbage to your console when it tries to read from certain directories. It also isn't near as intuitive as locate and takes longer to write-out. You're right that it is better than the graphical way though!
locate is fast because there's a cron job that does the heavy lifting of scanning and indexing the filesystem. Without that, find is about as fast as PS.
Yes and it puts it in a database updated regularly for fast access. I'm not sure why this isn't default on Windows. How often does one need to search for a random file in the OS?