Is there a way that users can requests permission to projects and a notification is sent to project admin user and this one can approve or not the permission via email or click a link?
Nope, not that this moment. There is a feature request for notification self service at https://jira.atlassian.com/browse/JRA-43161
which you can vote for. Don't hold your breath however, we are very few that seems to want this feature.
We have accomplished it by creating a front end portal that handles all the request access for us (the portal supports 7 different tools and one of them is JIRA).
There is a public signup in JIRA, you can use that. What Jonas suggested above is for notification and is somehow similar to yours (just permission).
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