As for 1, is the most common word in speech. A synonymous kango is . If you go far (e.g. to a foreign country) on a permanent basis, can be used as well. When you move from Tokyo to Osaka and back to Tokyo again, this can be described as
* .
Here you cannot use . When you do , usually you'll never return.
2 and 3: _to move from A to B_ is usually AB(). B is not impossible, but much less common.
For 4, no. in a similar usage would mean _to travel_. E.g., () means _(I) travelled from Tokyo to NY._