Read about Duplicate installation and select the part where URL changes.
TL;DR you should change in the elgg-config/settings.php
$CONFIG->wwwroot = 'http://your.website.com/'
and update webserver config.
Then run upgrade.php
That's all.
I also noticed the db password is in clear text in the config file which concerns me.
Don't worry about this - Elgg is very secure framework.
Anyway, I suggest to set chmod 444 and chown localuser:localuser (where 'localuser' is second user after 'root' in your system) on elgg-config/settings.php after installation (not before).
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Security issues should be reported to security@elgg.org!
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