Can the Autocomplete delay be lowered in forms? I have seen that the autocomplete widget in Forms API is started when I finish typing, or when there is a delay between one key hitting and the next one. Could it be configured so it is launched as soon as I press a key, like in Google Autosuggest or other search boxes?
As Clive suggested in a comment major part of the delay is because of the time taken by your server to populate the dropdown list. This generally happens because Drupal has to load all the enabled modules and do a complete Drupal bootstrapping. 

In special cases like Autocomplete responses that may not be necessary. Hence you can load only what is required and do a minimal Bootstrapping. 

You can check out the details of how this is done on this page.

Note : This involves custom coding and will not to perform any access checks unless you manually do it.