Getting Drush to play with MAMP and Acquia
when User°1 tries to start Acquia Drupal he just gets an alert box saying that the Apache server failed to start - nothing shows up in the Apache error logs (the MySQL server starts ok though).


Have you ensured you are only running a single apache process as OSX ships with it's own version and MAMP also has it's own. You can confirm it by running ps aux | grep apache in your shell.

Additionally, you can check which version has priority on the system (based on $PATH) by running which apachectl in a shell (example output).

$ which apachectl
/usr/sbin/apachectl


Which will help you determine that if there are conflicting version trying to run, who will be serving the requests.


  I've done everything I can to get this working, in particular by using the alias command
  like so:
  alias drush='/Applications/MAMP/bin/php/php5.3.27/bin/php 
  /usr/local/Cellar/drush/6.2.0/libexec/drush.php'
  but all to no avail.


I am not sure whether you should be executing that drush.php file directly as all of the installations I have ever completed all point to an executable that I usually move the /usr/bin or /usr/local/bin for system wide availability - But then again, I haven't tried installing drush 6 yet so that could have changed.

If you do a bit of development and don't like dealing with issues like this, I recommend you look at virtualising your environments using a tool such as Vagrant. Doing this will allow you to build an isolated development environment where you can configure the environment then package it for reuse should you ever need to reset it.