Does Homebrew install use SSL/TLS?

You can't know for sure, at least not based on the information you shared in the question:

• It's a https connection so it should be secure
• Nevertheless you could connect through a network which tricked/forced you to accept a new certificate and then performed a man-in-the-middle attack
• Somebody could have tampered with the script on Github, resulting in an attack within the script you've downloaded

In addition to the answer by @nohillside:

can someone please explain each of the options, flags, switches, etc. included in the command above?

Here's the install command-line:

/usr/bin/ruby -e "$(curl -fsSL https://raw.githubusercontent.com/Homebrew/install/master/install)"

Here's the breakdown of the various options (from the respective man pages):

ruby flags:

1. -e: Specifies script from command-line while telling Ruby not to search the rest of the arguments for a script file name.

curl flags:

1. -f: (HTTP) Fail silently (no output at all) on server errors. This is mostly done to better enable scripts etc to better deal with failed attempts. In normal cases when an HTTP server fails to deliver a document, it returns an HTML document stating so (which often also describes why and more). This flag will prevent curl from outputting that and return error 22.

2. -s: Silent or quiet mode. Don't show progress meter or error messages. Makes Curl mute. It will still output the data you ask for, potentially even to the terminal/stdout unless you redirect it.

3. -S: When used with -s, --silent, it makes curl show an error message if it fails.

4. -L: (HTTP) If the server reports that the requested page has moved to a different location (indicated with a Location: header and a 3XX response code), this option will make curl redo the request on the new place.