Installation Newbie Questions

Create a new folder and call it what you want, then upload the files and install from there.
Once installed, go to Options – Writing and delete pingomatic from the box. That will stop the pings as you play with wp.
Making it non-accessible ? Well if you don’t tell anyone, we won’t know ??
Aside from that, you could use a .htaccess file ( https://www.clockwatchers.com/htaccess_intro.html )
but then if you post here and need a hand, you’ll have to tell us the password.
And if when leaving your testblog, you click on somewhere safe (like another page in your own site) before going around the net, then no-one can find your site through a http referrer in your browser.

That new named subfolder would be in my Public html folder?

Yup ??
That’s where all your website pages will go.
If you don’t put them into a folder (directory) then if someone goes to your site, the ‘index.php’ file will be loaded
Put them into a folder and unless someone knows it’s there, or wants to take a daft amount of time guessing directory names, no-one will ever know it exists – except Google and other Search bots, but to be honest you sort of have to live with them. Google may obey some rules, other bots ignore all the robots standards.
Either way, you’ll still be able to play with the install, get it looking good etc.