Clash-of-clans – Clan castle during attack

Yes, this "tiny castle" is in fact linked to their Clan Castle.

When in a clan, you can request troops from your clanmates. If you have troops in your clan castle, they will automatically defend your base if it is attacked and the attacking troops enter the clan castle's radius.

Alternatively, you can deploy these troops to bolster your own forces during a raid. They will show up in the troop selection bar with an icon denoting your clan's shield. Deploying them is an all-or-nothing affair.

Either of these two things will use up the troops in your clan castle.

The troops in the clan castle indeed defend each attack.

You can be attacked more than two times in a war, but your clan castle is always full for defending against those attacks, full of whatever was in the castle at the end of the war's preparation phase.

Additionally in war:

1. Heroes are always active to defend your War village.
2. Defenses like Xbows and Inferno towers, and traps are preloaded
3. Any defenses under construction are active in war, unlike your home village. In fact, any defense STARTED prior to the end of preparation day is active and defends your war village.