From my perspective.
Temperament is a predisposition to various behaviors. ie. If you have a dog that is sound sensitive, they are going to cringe, run away, etc. if they are caught in a thunder storm. Dogs that aren't sound sensitive won't act the same way, necessarily.
Make sense?
Behavior a result of temperament and training? Up to a point and only up to a point.
There are some dogs that might be fearful about something. You can SOMETIMES desensitize these dogs to whatever stimulus is causing them to be fearful. That being said, there are some dogs that will never be able to be desensitize to a fear.
Behavior genetic?
That's something that responsible dog breeders discuss all the time.
From being involved with dogs for 40 years, 30 years as an instructor of obedience and search and rescue work, my feeling is that puppies can be tested to some degree to see if they are predisposed to behavior (caused by their temperament). You have to keep in mind that all puppies are individuals, just as all humans are individuals. Twins don't have the same temperament.
All of the above ignores the fact that some dogs are truly hard wired crazy. Just as some humans have severe mental problems.
----------------YOUR fear of spiders and tornadoes is LEARNED behavior. It has nothing to do with genetics. Genetics might make you more sensitive to sound or light. The sound sensitivity might make you fear tornadoes. Off the top of my head, I can't think of anything (except touch sensitivity) that might be genetic that would cause a spider fear.
What nature gives you, you can't remove? That depends on what you're talking about. I can take a dog with a VERY high prey drive and teach them to control it, but yes, you can never remove it.
Train, manage or euthanasia? For me, it's the first two versus the last. Easiest decision relates to human aggression. If you can't get it under control, you've got a ticking time bomb. Do you want to be responsible for someone getting REALLY hurt, or KILLED?
Inga - Thunder. Might want to look into "Thundershirts". The theory behind it relates to the work that Dr. Temple Grandin (her autism & cattle behavior books) did in calming down cattle.