I'll write no, yes, and maybe.

Windows Update when I type in that box to the right of the start button finds windows update so checking for "Windows Update" in the "All Control Panel Items" does indeed not find it. But Windows Update is still in the OS. I found it.

As to the download and install automatically, that's true for Windows 10 Home, but can be tailored in Windows 10 Pro so when asking 10 questions you need to ask for each version. The question of updates has been in the news and beat about a bit so I'll pause here.