If one passes the Bar exam in one state, is he/she qualified to practice in any State? Logic says yes to me.

No, as far as I know each state has it's own exam. I believe you can only practice in states where you are admitted to the bar of that state.

That is correct. Each state has its own requirements. Likewise, even, in the US Federal system, there is no single bar examination that permits practice in all Federal courts.

In some states, you may be eligible for admission absed on reciprocity or request a temporary admission for specific cases.