The index of changes, which is easier to look through than reading every single changes post, is here:
http://aurora2.pentarch.org/index.php?topic=10666.04) I've been neighbors with an alien race for ages. Language is understood and diplo ships are there. But our relationship is still 0. Are there some (non-spoiler) races which don't ever feel like getting friendly?
Very high xenophobia will essentially prevent diplomatic relations from increasing, so check your race stats.
Anyway, I don't quite get the command HQ system - if I can just enter any number (max. command tonnage), what's the point then?
For Ground units, if the HQ size is lower than the unit it commands then the commander bonuses are reduced proportionally.
Larger HQs cost more to research and build than smaller HQs, but provide their bonus to more units. They are also larger, up to 250T max.
A chain of HQs provides a portion of their bonus down the chain. Also you can use the "Load all sub-units" checkbox to load a whole formation with one order. Finally it cleans up the ground window.
10) Leftover damage (after destroying a ship component) is applied "sideways" to other components, or wasted?
AFIK left over damage gets applied to the next component, as determined by the DAC. Components with 0 HTK can get chain exploded, ie all the damage keeps transmitted.
11) With no water on a planet, terraforming is kind of pointless, right?
It takes longer. First you add water vapour, the water vapour slowly condenses out of the atmosphere and the hydrosphere increases.
12) Are missile-based planetary defenses possible?
There are no missile based PDCs or STOs. You can build stations, but you need a Naval shipyard because 'no-armour stations' can't have military components.
13) Can I scrap ground units and get minerals back?
In 1.13 and lower you can delete formations but you get nothing back. In 2.0 (aka 1.14) scrapping will give you 30% of the cost and minerals back.
14) Can I stop e.g. fighter factories from employing millions when I don't build any fighters, other than shipping them all to the next moon?
No, you need to move them. If it's any consolation, they do generate you wealth.