Clearly, the caster can select the initial target.  Does the caster also get to choose the additional targets, or is that up to the DM and/or random?  Will the secondary targets always be "enemies" or are allies also subject to random selection?

It seems the wording implies that the other targets are also chosen.

If you are a Storm Sorcerer at high levels (18+), wearing a blue dragon mask, could you cast this spell in the middle of enemies, and target yourself to heal while attacking the enemies?

If you already have immunity to lightning from another source (Wind Soul), the blue dragon mask makes it to so you heal HPs in the amount of half the damage you take.

Just... The implications at high levels.

It would certainly seem that way, however I'm sure there are more reliable drain-tank builds. Could be a cool thing to do in a pinch, but I wouldn't build an entire character around it.

Why don't druids get this?

Because magic lightning that unnaturally jumps between targets to an accurate degree isn't in theme for the chaotic nature based spellcaster

why can't I get this spell to list for my 11th level Bard. should be available with my spell focus?

Since you are immune to lightning damage you would take 0 damage, so half of 0 would be 0. So you would not heal anything.

Because you get Magical Secrets at lvl 10 where you don't have a 6th lvl spell slot, at lvl 14 you can get it

Considering chain lightning can target objects, I'm just imagining a group of 4 paladins raiding a lich's palace and he just zaps their armor away and watch as they flee naked.

Quote from Cloudstorm >>

Considering chain lightning can target objects, I'm just imagining a group of 4 paladins raiding a lich's palace and he just zaps their armor away and watch as they flee naked.

Can't do that, general rule of DND objects carried or worn can not be targeted separate of the creature wearing or holding them

I'm not sure I agree that the sorcerer gets to choose the "three other targets".

I wish the wording on this spell was clearer. It should read either:
"You create a bolt of lightning that arcs toward a target of your choice that you can see within range. Three bolts then leap from that target to as many as three other targets of your choosing, each of which must be within 30 feet of the first target. A target can be a creature or an object and can be targeted by only one of the bolts."
or
"You create a bolt of lightning that arcs toward a target of your choice that you can see within range. Additionally, as many as three bolts then leap from that target to the three closest creatures, each of which must be within 30 feet of the first target. The initial target can be a creature or an object and can be targeted by only one of the bolts."

I see this more like fireball. Whoever is in range gets hit. Friend of foe.

Has there ever been an official ruling on how to interpret this spell?

You are right, the wording is a little clumsy. I however would say that the targets are chosen by the caster as it's not specified they are chosen randomly. Otherwise the secondary targets could be random dungeon clutter and a waste of a higher level spell.

I have no idea, I totally think they should

The terms 'target' or 'targets' implies its deliberate. Its a point chosen with intension. Otherwise it would say randomly as it does in different spells.

Not to mention if a 6th level spell was that dangerously unpredictable it would be so niche to use for any PC who typically travels in a group.

Quote from ARedLlama >>

Since you are immune to lightning damage you would take 0 damage, so half of 0 would be 0. So you would not heal anything.

The Blue Dragon Mask (and others like it) give resistance unless you already have resistance from another source, then it increase to Immunity. And if you already had immunity from another source the mask adds Absorption.

Which means you always have immunity before gaining that property so it seems pretty clear the intent is 'half of the attack's lightning damage' not 'half of the lightning damage you actually took (because that's always 0 and this ability wouldn't need to exist)'.

All that said from the original question of "wouldn't that be insanely powerful?" - yes, sure. But EVERYTHING is insanely powerful at level 18, especially once you start throwing in legendary items.

Does the material components have to be a bit of fur, three silver pins and either a piece of amber or glass or, a crystal rod

or is it a bit of fur, three silver pins and a piece of amber, glass or crystal

It is the first one:

1. a bit of fur

2. Three silver pins

3. A piece of amber, glass, or a crystal rod

The use of semicolons (;) splits the necessary component groups up.

why would this spells School be advocation?

Read the description of the blue dragon mask you would head if you had immunity befor and the blue dragon mask on