A star base acts just like a planet when it comes to navigable ship range.

  Influence bases can be built anywhere and project influence around themselves just like planets do. They're more efficient if placed near your own planets because they provide a boost to that planet's influence growth as well.

Yes, just like planets, and "not really". However, the effect on your influence on another empire's planets will be enhanced the closer they are to that empire's planets. They can also be placed inside another empire's zone of influence (if they haven't taken some action to preclude your doing so), but some consequences COULD occur (such as war or other dire reactions by that empire).