Hello and welcome to LinuxQuestions,
Apparently you either installed from the NETINST CD the basic install of Debian and didn't choose to install the Desktop Environment when completing the install (final step). If you'd had done so then you'd have a graphical user interface. Right now you only have your console as it seems. You can install a complete X environment from the console but it will take some time over a slow connection to download all the packages you need.
I don't know all the commands exactly but you could start from here
in my opinion.
What concerns your other question, if your running from a liveCD/DVD then of course you can write to your harddisk but you'll first have to mount it.
You'll just have to find out on which harddisk/partition you want to write using
and then when booted in your liveCD/DVD create a directory and mount the partition on that directory:
mount /dev/sda1 /drive
if your partition is on sda1 of course.