I'd agree. My assumption is that "owning nuclear weapons" is too broad and does not support "weapons would cause great harm. . ." I think Nuke weapons great harm → Supports → Wrong for countries to own*

I would agree.

Tigers are aggressive (Premise) →Supports → That not every mammal is suitable to keep as a pet (Conclusion)

Because Tigers are aggressive, they are not suitable to be a pet.

Like it says above: "Support means increases likelihood of truth". Aggressive Tigers supports the argument that not every mammal is suitable to keep as a pet.