In my experience, no they do not deal friendly casualties when you bombard battle-locked units. Of course using artillery or air power would put you on the safe side, but I personally wouldn't hesitate to use rockets.

Nevertheless, I think it is a fair assumption to believe that your infrastructure will be damaged. Logically, every "team"' 's attack will have an affect on the buildings (seen in their combat stats), it is therefore normal that rockets do the same.

Same experience here as described by darksoul 111, never observed that rockets caused damage to own or neutral units.

So far I have fired 2 Lvl 4 rockets against enemies in my own provinces, to test it shortly after the possibility was introduced, and my own buildings have taken a bit damage, but that's a long time ago now - maybe it will be time for a few new tests ..

1) Correctly..
2) Correctly..

..and that results in:

1a) Allies, own or neutral units located at the same point where the rocket hits, aimed at an enemy, will not be damaged.

2a) If enemy units are attacked with rockets while they are located on neutral / foreign territory caution is required, because as is well known the most damage energy of rockets hits the buildings and the terrain (lowers the morale), and it's not only so in the province center, and if area damage is too high, the TILT SENSOR will trigger war.
I can't tell you when it will triggered exactly, anyway it's not much scope...

I have been the victim of a friendly fire rocket attack, and I lost several units.

A coalition mate and I had eliminated Caucuses, and had found and sunk one submarine of theirs already. Caucuses had no provinces left, so I sent several units the length of turkey which I had already conquered to get to fresh targets in western Europe. Being that we owned everything in a couple thousand clicks I did not consider any danger in the water crossing at Istanbul. Well caucuses had a sub parked there, so my units marched by one's and two's to their doom. I did catch the last few units being attacked by the sub, and my coalition mate had the idea to use a L2 rocket on the sub as nothing else was within 12 hours drive or flight. The rocket eliminated my two convoys that were locked in battle with the sub, and one that was just half embarked on the Izmit shore.

It did not scratch the paint on the sub.

My units were lost at that point anyway as they could not escape the sub and no other unit close enough to rescue them was available. So really had nothing to lose. Of course he launched the rocket before I could check the stats and find that a rocket had zero points against submarines.

This was also shortly after the recent change that meant rockets had a daily oil upkeep, so he was looking for targets for them, having built them before the upkeep was instituted.

So to sum up:

Lesson #1: Rockets do not damage submarines

Lesson #2: Convoys are fragile, and damaged by friendly fire rockets.

Lesson #3: Submarines do not go inactive just because you conquered all the provinces of an enemy.

1) Correctly

2) Probably your buddy clicked not accurate and shots the missiles at your convoys?
(maybe because it was indicated to him at the Sub-Target that they would not cause any damage ... )

3) Correctly

Hmmm, Maybe I should re-evaluate why I came in second in that game.