I am not exactly sure what you are trying to do. In particular, I don't understand what you mean by "merge." Others might know, but I'll start with a few questions. I run MAMP 5.1 on my Mac, but only for experimental purposes.
It appears that you have MAMP5.2 successfully running on your Mac? Right? If you go to localhost in your browser, you get the MAMP Welcome screen.
No, dragging Moodle to your Mac's application area won't do anything. Moodle needs to be in your htdocs folder within MAMP.
Before installing Moodle in MAMP, you need to create a Moodle database, typically/simply using phpMyAdmin. And then you should create a folder called moodledata in your "data" folder of MAMP.
Finally, go to localhost/moodle, and moodle's install will start.
Moodle is not a Mac application. It runs in a web server environment.
Hope this helps.