I am quite sure The Night King can see just like Bran hence why the WW waited for ages until attacking even if another reason was the lake getting refrozen,
he prepared Ice Spears because he knew dragons would be coming his way and he wanted to snatch one as a mount.
Why not Drogon? I guess he wanted to throw it at the one flying causing lots of damage to his minions + being distracted doing so.
I think Drogon and Dany were looking at around NK way so maybe she would have shouted and Drogon would have melted the spear with his fire.
The chain thing just reinforces my speculation, where'd they get such a huge chain and why at all? To bring the wall down? If so, alright... Else probably NK planned everything ahead for getting that Dragon mount for himself.