A Druid (Melltas) who is deaf and dumb joins your party on the second island (Gratogel). However he has a close relationship with an Iskai of your party (Sira) who speaks for him if he wants to get new spells. But this trick doesn't work for combat training - I found no way to get Sira to speak for him to the trainer and so the Druid has lots of training points available but apparently he cannot use them. What am I missing?

The trainer in Jirinaar is the only one willing/capable to improve Mellthas' combat abilities. You can't go back there right now. However, once you finish the main quest on Maini (the next island), you'll get access to a new travelling method that allows you to go to any island you want.