As far as I know, there's no way to install the Homebrew package manager without root.
But if your goal was to install Bitcoin Core, I'd recommend pulling the source through git (like you've done) and building it locally, anyway.
I pulled the source through git. I will like to ask is $brew command line doing the same thing $ sudo does ? Because pip isn't install anything for me on my mac command terminalBut if your goal was to install Bitcoin Core, I'd recommend pulling the source through git (like you've done) and building it locally, anyway.
brew: OS Package manager.
apt: OS Package manager.
pip: Python package manager.
sudo: Execute command as superuser / root.
git: Version control system / VCS.
And how to enter your password on the command line is what I've answered in the very first reply. Was something unclear about that?