The default package manager on Red Hat Linux is yum, not apt-get. Even though one of the error messages you posted mentions Debian/Ubuntu, I'll assume you're using a Red Hat system like your question suggests. You can probably confirm your Linux distro by using one of the following commands:
There is a Plone documentation page for Preparing to install Plone with notes for CentOS, which is essentially a free variant of Red Hat. That page suggests the following yum install command for dependencies for Plone 5:
yum install gcc-c++ patch openssl-devel libjpeg-devel libxslt-devel readline-devel make which python-devel wv poppler-utils
Or for dependencies of Plone 4:
yum install gcc-c++ patch openssl-devel libjpeg-devel libxslt-devel readline-devel make which python-devel
There are, of course, caveats for whether or not you're using the system default version of Python, so you'll want to check that out. You should also make sure that you're looking at the correct documentation for the version of Plone that you're trying to install.
Once you've installed the dependencies, then you would run the installer as you tried to do previously, assuming the arguments are correct:
sudo ./install.sh --target=/home/admin/Plone --build-python zeo