1) No vessel may Initiate Jump Point! or Activate Jump Gate! and shoot in the same round. See the Special Actions for the full wording.
As Burger says you may not shoot through a vortex (e.g. realspace > hyperspace), however the vortex does not block line of sight so you can shoot a target behind the template.
2) A vortex may be maintained for up to 3 turns by using the Initate Jump Point! special action. Once a Jump Point is removed, a ship needs three turns to recharge it's Jump Engine before it can open another Jump Point. See Jump Points in the Advanced Rules section.
3) As Burger says, the quickest multiple jump points can be opened is every 4th turn.
4) You may fly over it, and the vortex backwash only occurs when a jump point is created. To use a Jump Point the following conditions must be met. Your 'side' must have created the Jump Point; You must enter from the Front arc; The vortex must be of the right direction (realspace > hyperspace is yellow and hyperspace > realspace is blue), you cannot use a realspace > hyperspace vortex to bring ships from hyperspace into realspace.
It is worth noting that the Shadows and the Ancient Triumviron use special hyperspace mechanics.