When you go on the website you need first to use the following password: cerberus
I’m using Ajax search pro and for some reason it doesn’t work well.
If you go on the homepage you will see for example that there are 2 suggested keywords. Only “training” works and it show just part of the results. As I’m mainly using search based on post titles and categories I’m surprised to see it doesn’t find the categories.
You haven’t selected any taxonomies to return (in your case project categories). You can enable search in terms on the General Options -> Sources 2 panel, and select the taxonomy you would like to search as well.
For the recruitment I can’t see any published posts, only private ones. Private state is not a default in wordpress, thus the plugin does not recognize it. Do you also want to search in private posts as well?