No. 100% of humans are addicted to dopamine. When you shoot drugs, you arent usually feeling "good" because of the drug, so much as the drug's influence on dopamine levels. (Some caveats apply-- some drugs simulate dopamine in the brain.)
Inaccurate. Drugs - legal or illegal - do not, generally, work directly. Caffeine for example, does cause an increase in cAMP levels (among others, the stimulatory effect is something else) - but it does so by inhibiting the natural mechanism by which it is degradated. Which you have mentioned, but implied it's a rare thing.
It's the *primary* way drugs work - it doesn't matter if it's stimulation of synthesis, inhibition of degradation, increase in sensitivity to the target chemical or whatever. You could actually inject pure Dopamine, it's available commercially, though presumably not to anyone who walks in and demands it.
Neurochemistry is also *far* more complex than loldopamine. Dopamine is responsible for *seeking out* the stimulus, primarily, which is not the same thing as the stimulus being pleasurable.
And while we're at it, a lot of drugs aren't even dopaminergics - weed, notably, is a serotonergic, so is pretty much most of psychedelics. LSD is both dopaminergic and serotonergic, but it's very rare in that regard.
Typical dopaminergics, such as meth or cocaine, are indeed highly addictive, but so are opiates - which are not dopaminergics.