No; invocation prerequisites are based on warlock level.
Eldritch Invocations are based on your Warlock level, not your character level. Per the description (PHB, 110):
If an eldritch invocation has prerequisites, you must meet them to learn it. You can learn the invocation at the same time that you meet its prerequisites. A level prerequisite refers to ...
No you would not
Sculptor of Flesh
Prerequisite: 7th level
You can cast polymorph once using a warlock spell slot. You can’t do so again until you finish a long rest.
You would need to be at least a 7th level Warlock. The character level does not matter for the prerequisite.
As stated on PHB pg. 110
If an eldritch ...
The wording is not vague
You always take the maximum value of any dice rolled to heal you. If someone casts a spell that heals 2d8+3 hp to everyone in 30 feet and it affects you and they roll a 3 and a 1 you heal 19 hp and everyone else affected heals 7. You treat dice rolled to heal you as if they rolled their maximum value for you. The source of the ...
Yes, that seems to follow from a literal reading, though I can't think of a time it would matter.
Though, as noted in the question you linked, Devil's Sight arguably works only in total darkness. Eyelids are not completely opaque to light (and you wouldn't want them to be) so we wind up in the odd situation that the Warlock could only see his own eyelids ...