Is SQL Plus only an environment that
is able to connect to an Oracle server?
Yes, SQL*Plus is not very useful unless you can connect to an Oracle database server.
I'm asking this because I just started
learning Oracle's SQL syntax and I
don't have access to my faculty's
server from home. The only solution I
found so far is Apex since I'm not
planning to install a server on my
laptop.
If you cannot connect to your faculty's database server from home, you have no choice but to install your own server somewhere. Apex only runs on an Oracle database server.
However, it's not too difficult nowadays, as long as you follow the installation instructions carefully.
Another option is to get a free account at apex.oracle.com. You'll be able to use Apex's SQL interface. I don't think you can connect to it using SQL Developer, though.
Alternatively, you can start up a simple pre-prepared Apex instance on Amazon's EC2. With this option, if you open the relevant port (1521) you'll be able to connect to it using SQL Developer.