It is somewhat faster, but still too slow I think.

A flat 4 HP per turn is gonna get real tedious real fast when ships start to get more than 100 HP.

It needs to be a percentage, 2% when out of combat (with a minimum of 1hp), and 10% when in orbit (with a minimum of 4hp).

One, those are both late game technologies, and two, they require space on board a ship as well as resources. Plus, they only work in combat, they don't make repairs happen any faster out of combat! Same with Iconians' auto-heal -- it's often better to enter combat with pirates just to repair your ships!

Imagine you found a Ship Graveyard with your Survey Ship, and now you have to repair it before finding another. That's going to take 60 turns, or 20 turns with the ship in orbit around a planet, not doing its job. Repairs take way too long.

Would be nice to have a "return to nearest base an repair" button, that sends your ship to the nearest starbase,  shipyard or planet and once repairs auto rejects. I always forget where I sent them or forget I have ships repairing on a planet.

I think you should be able to dump production into repair - using shipyards. So you can repair in 1 turn if needed, but it will basically cost you most of the production used for the ship.

The game also probably needs a repair module for military starbases, available fairly early. 

How about, shipyards can automatically repair using your production. You send a damaged ship to a yard. It jumps the build queue and starts using your production for repairs. When repaired, automatically ejects like any other new ship.

Repair cost would be the same as the build cost for a new ship of that exact model. Less the non-damaged health.

Keep the current slow, planet, starbase, crew repairing. Those are production cost free.

Not a bad idea. Replacing damaged weapons systems and rebuilding hulls does require industrial capacity.

You can just upgrade the sh to itself.  Is cheap, takes a few turns and fully healed.

It's a compromise, but I can see where you are coming from. It's better than what it was.

Out of combat (enemy or neutral space) should have a 1% or 1 Hp minimum.

In your own space = 2% or 2hp per turn.

In orbit should be faster,

in a shipyard that is building a ship should be faster.

In a shipyard with an order to repair a ship MUCH faster.

Unless the AI is coded to use this as well I actually don't like this

I like this. Although the danger is there that a ship will be repair from 1HP--> max in 3 turns. Let's say an AI has a really good fleet together and sets course versus hostile fleet 1 (which will be defeated lossless albeit with loss of some HP from one of his ship), afterwards it'll target fleet2, fleet3 etc. With high enough repairability the fleet will always be repaired back to 100% and therefore, never loose a ship.

So I think the game should reserve some strong repair reserve if you use your ships defensively (own territory, shipyard) while there should be a penalty (or no bonus) in hostile territory.

This isn't particularly difficult to code. At worst, it's a bunch of if statements, or if you're smart about it you could do something like

[repair rate this turn] = 0.05*max(1, floor(10 * [current HP] / [max HP]))

[HP restored this turn] = min([max HP] - [current HP], ceiling([max HP] * [repair rate this turn]))

and you can toss a min(x,y) in there if you wanted to cap the repair rate below some level. I don't know that we could do this in the XML files, but it's certainly something that someone who had access to the game code could implement fairly easily.

I personally would prefer something more like

[HP restored this turn] = min( [max HP] - [current HP], max(1, ceiling([repair rate] * ([max HP] - [current HP]))))

or

[HP restored this turn] = min([max HP] - [current HP],

min( [max HP] - [current HP], ceiling(F([current HP], [max HP])*max(1, ceiling([repair rate] * ([max HP] - [current HP]))))))

where F([current HP], [max HP]) is a scaling factor such as [current HP] / [max HP] or (0.5 + 0.5 * ([current HP] / [max HP)^2) which slows the repair rate when the ship is badly damaged.

This gets the ships back in action relatively quickly but makes it take a bit longer to restore a ship to peak condition, whereas your model leaves ships out of action for a relatively long time but finishes quickly. Probably a matter of preference, but I tend to feel that a repair model that makes it so that your ship is in usable condition relatively quickly but takes longer to complete all repairs is more interesting than a repair model that makes it take a long time for your ship to be restored to usable condition but quickly completes final repairs. The former incentives risking damaged ships, the latter incentivizes restoring them to perfect condition before sending them out again.

Hmm they do repair faster in orbit,  hadn't actually noticed that, will have to test.

Personally the biggest change I would like to see, is the option to 'repair' in a yard. (likewise upgrade).

So that instead of building a new ship,  a ship could go into the yard and get repaired at a fairly fast rate (or hell even at the % damaged vs Build time).

As 'free' repair  the existing is ok,  but Even relatively minor damaged ships, I find I am often scrapping and building new ones,  where I would much rather (mind set wise) repair existing ones.

(especially if 'experience' is ever added in for ships)