Yes, Claw learned his talents from trial and error. 

Claw doesn't know what a molecule is, but he can see vibrations all around him by switching to a magically-powered type of *'meta sight'. At some point, he probably messed around with various frequencies and found that strange (and rather destructive) things unfolded when he practiced this art on individual objects or living creatures. Granted, this is one of the higher-end applications for Claw's Echoing abilities (as well as the possibility of causing spontaneous explosions to occur, though without the flame effect), but it's within the realm of possibility.

Unsure if I'll even use something like that though. From a realistic standpoint, he'll only use things that are actually useful to him. Making something explode isn't that useful given it draws unwanted attention to Claw's person, which is bad in a land where the Crusader extremist group (Shien told me about them) wanders about and where frightened villages and towns might decide to don pitchforks, swords and woodcutting axes to do away with the large canine-like creature that's been heard and seen doing undesirable things.

When I was designing the Echo, the idea was to create a magic type that was both a worthy blessing but also a terrible curse---one that grows in power with each use, and that cannot be rectified in any shape or form. I don't want to go down the cliche route and claim that Claw gradually loses his sanity or something, but I originally had it to where Claw's own essence slowly degraded as he made use of his otherworldly talents, opening him up to death's waiting embrace and where his own soul will not go on to the afterlife (if such a thing even awaits the del-korm species. I don't think I ever designed one). 

Also, would it be acceptable to have Claw take a page out of the Xuhrl-njok's playbook and consume the hearts of living creatures to power his magic and give it the capacity to grow in strength?

*I might alter this to where Claw can feel and hear these vibrations. The idea of 'seeing' and not 'hearing' kind of clashes with the overall theme I'm going for anyway.