How does combat affect your companion?

I've seen tips that my companion is in trouble or that I should give them a Stimpack, but I've never had an issue of my companion dying.

Can companions die?

I've also noticed that sometimes they will just walk in my line of fire and I'll end up shooting them a couple of times with a machine gun or something.

Will they change their view on the relationship if I shoot them?

Followers can not die. Also noted in this article about companions that can't die.

Good news: no matter what transpires out there in the wasteland, he cannot die.

In fact, none of the companions that may accompany you on your quest across post-apocalyptic Boston can die. Speaking with IGN, Bethesda's Todd Howard discussed the now-immortal companions, a decision the development team made to better serve the player.

Since they can't die, doubt shooting them will bother them much.

Contrary to popular belief, some companions can, in fact, be killed.

From the wikia page regarding Fallout 4 companions:

Unlike Fallout 3, companions are marked as "essential" when acting as active companions, meaning they cannot be killed. If incapacitated, they will automatically heal after combat ends.

This leads to the following point:

Some companions lose their essential status when dismissed. They do, however, remain protected like other settlers and cannot be killed by NPC attacks (only by the player or their active companion or related action)

and

Some companions lose their essential status upon reaching the lowest level of affinity and leaving the player character.

It appears that the "killable" companions are the following:

Danse, X6 and Deacon are the only companions who can be killed by the Sole Survivor if they're not following the Survivor.