How do you manage multiple vessels?

Rally points do work but you need to turn them on for the planet producing a ship that you want to fleet up.  You can also use the governor screen to tell planets with no rally point to send ships to a particular rally point, or change the rally point for all planets producing a particular design.

When you create or edit a rally point (RP) you can set it to Fleet.  This means that when ships arrive at the RP they will join up with existing fleets if there is room, or create new fleets automatically if no fleets have room.  It will be up to you to direct them after that, however.

You can set an RP on an enemy planet or starbase and ships with a rally point order for that RP will attack it.  However any ships that have finished moving to that target will obviously not attack again even if you move the rally point.

You can also select multiple fleets at the same time and give them an order. Hold the shift key and draw a frame around the fleets you want to select. After that is done, just right-click on the destination.

It isn't necessary to manually move the ships each turn, if you want them to go to a distant location. Just click on the destination and they will automatically move at the end of each turn until they arrive.

Regarding the combat animation: You can disable it in the Options under Interface. Just deselect 'Full Fleet Battles'. If necessary, you can also disable the short battle sequences by deselecting 'Show Battle Sequence'.

Is there a "move all" button? I have a miner on automine, 2 scouts on auto scout and one surveyor flagship on auto. Is there a way to make them all move at once or do I have to right click on them all to get them to move.

Thanks

No, there isn't. However, they will move automatically once you hit the Turn button, so you don't have to move them all manually.

The only time spaceminer/scouts/surveyors stop when on auto is when they can no longer improve mines (need space mining 1-3),scouting when they either max their range or uncover the entire map (depends on life support/range/size of map),surveyors/flagships go into standy mode till more anomalies pop up which they do throughout a entire game unless disabled in game menu. as Gaunathor said^

  In the "Civilization Manager" screen,  click the "Governors" tab.  There you can reroute all ships of a given type (I have used this mainly for mobilizing my transports to an unexpected new warzone;  I believe they can only be rerouted to a rally point).  There you can also multi-change other stuff such as shipbuilding and ( as MarvinKosh replied) colony rally points.

  I click "launch all ships" at the beginning of a turn, then I put all lone ships on "guard" (shortcut key "G") or join it into a fleet (select all then shortcut key "F") with a previous guarding ship.  Inefficient having idle ships but they can all be moved later as one fleet.  Best for constructors because also the starbase upgrade window only needs to open once for the whole fleet.

[EDIT 10 May:]  Easier manually,  but also easier for older computers which are slowed down by many individual ships with orders.