You need to check server error logs. It's likely that you have some conflicting configuration of rewrites or some other problem. Need to see exact error.

You might see also: https://community.elgg.org/discussion/view/762524/500-internal-server-error-on-install though it doesn't seem useful thread.

Due to rewrite rules of each "software" (joomla, elgg) the installation of software within a subfolder of another software causes trouble usually. You better install elgg in the folder url.in/community and joomla in the folder url.in/site and redirect your index-page to url.in/site.

Another way could be the usage of just one software, you could think about using either joomla or elgg...

Can we please get the error first? Last time we had this problem, we couldn't recreate it. If we don't recreate it we won't fix it.

new custom plugin or already available plugin?

If you wish to install an existing plugin (for example from this community) look at http://learn.elgg.org/en/1.x/admin/plugins.html

If you wish to learn how to make your own plugins start looking at http://learn.elgg.org/en/1.x/tutorials/index.html