Who was the Captain of the Guard at the outer gate of Gondolin?

Nice new avvie, luthien-elvenprincess
 

Elemmakil?

Yup.

Ok . . .
 

What does the epessë of the first wife of Finwë mean?

Serinde = Broideress.

Adequate.
 

Your play.

With what event did the First Age start?

Beginning of the First Age
 

The Return of the Noldor to Middle Earth.

Not really. That just happened to happen at the same time.

I'll stand by my answer. You could mean Dagor-nuin-Giliath, of course, but that battle was entirely dependent on Feanor's return, thus also rendering my initial answer correct. Or you could mean the Awakening of Men, in Hildorien. However, as this is hardly so clearly a defined occurence as the Return, again I'll stick to my initial answer. :)

The first moonrise

When the Sun and the Moon were destined to cross the sky, or rather began it

The moonrise is what I had in mind. Your turn, Estanesse.

An easy one, who killed Khîm.

Andróg.

That’s correct carry on

For what price did Gorlim trade news of Barahir's band with Sauron?

Meeting his wife.

Not quite.

To find his wife and to be set free with her.

Good.

Probably an easy one:

How many wounds did Morgoth receive from Fingolfin?

7?

no

8?

correct, Nightknight.

Seven during the battle and then one last blow, if I remember correctly.

Where is the giant Gilim mentioned?

Gilim the Giant of Eruman
 

I believe Gilim is mentioned in the Lay of Leithian:

Absolutely! I'm currently reading it, and it's great! :)

And now, I hand over the thread to you. :)

Thank you Sir Knight I hope you're enjoying it as I have :)

Next question:
After Turgon, who is acclaimed as the bravest warrior of Gondolin?

It was Galdor of the Tree.

Correct! Your turn.

Who were in the Great Wolf Hunt?

Hunting of the Wolf
 

King Thingol set out to hunt the wolf Carcaroth with the greatest of his warriors:
Mablung
Beleg
Beren Erchamion
and Huan the Hound of Valinor.

Yup, he did. And both Beren and Huan died. Please carry on. :)

I think we're on a roll Knight! I really wish Huan lived....

In what year of the First Age was Dior Aranel born and where?

FA 475 on Tol Galen.

I was thinking 470 but I'll accept it -- and Tol Galen is correct.

You may go on :)

Why did Finrod Felagund learn the language of Beor's people so quickly?

Because he could read in the minds of Men such thoughts that they wished to reveal in speech, so that their words were easily interpreted.