Lets assume character has 2def 1HP (current).

Enemy dares to attack STR2. He gets his Shadow card.

I say "Kiss my Arrow" and Exhaust my character to defend.

Than the shadow effect rises his STR by 1.  Now apart from murmuring "I'll kill You, I'll kill You, I'll kill You..." i see some options:

in hand I have the card (EVENT of course) that for some resources can heal some wounds and on the board lays Glorfindel with 1 res token on him.

So:

A) my character dies?

B) i can use any of my options?

C) I can use only Glorfindels ability?

D) I can use only my card ability?

This is actually a tough one and comes down to timing and what's allowed when.

From the rulebook: once you have identified the shadow effect (step 3), you go straight into determining combat damage (step 4). Crucially, these are two different steps in the process, which saves your character in this case.

Because on page 31, resolving attacks is in a green box, meaning "any player can take actions...between the game steps stated in the rules". This provides the window you need: between applying the shadow effect and determining combat damage, you can take actions. This would include the play of events (whose actions are not limited to other phases of the round) and use of Glorfindel's ability (assuming you have not already used that this round).