Am I right to suppose that the deadline for submitting the application form is 23:59 Central European Time on 15th February?

Don't you have to send it per post? I had to at least for the traineeship that I'm doing now and it might be difficult to find an open post office at 23.59

The deadline for submitting the online application form is 12.00 CET on 15th of February. And then after that like Aneena said you need to send your application via post, and your application need to be postmarked on the 15th. So after sending the application online the deadline for sending it via post will be the closing time of your local post office on Monday the 15th.

And by the way all this information could quite easily be found in the Traineeship webpage
http://ec.europa.eu/stages/information/application_en.htm#Infotab1