Is there a downgard swod?

Nope.

no only war axe and war hammer.

and shield, think it's stupid they missed another chance of having a really nice looking sword in the game, currently only like daedric greatsword.

If you are on the pc grab this mod

http://steamcommunity.com/sharedfiles/filedetails/?id=88521325

It adds sliver one handed sword, two handed sliver sword, sliver arrows and sliver crossbow bolts plus the sliver swords can be upgraded.

I started to use Skyforge Steel Sword. It looks very similar in style.

It depends if you mean Dawnguard as the faction or as the add-on . There is a sword for vampires if you beat Harkon.

Spoilers

I wish there was an Ancient Falmer Sword. No sword seems to match the Ancient Falmer Armor, and I wish there was a unique sword with a white sheath.

You could use http://elderscrolls.wikia.com/wiki/Chillrend_%28Skyrim%29 If you know where to go, you can get it without having to join the TG

I always thought dawnbreaker looks nice with ancient falmer

preffer the mod that adds a one handed and two handed version of the Litch King's sword from WoW.. God that thing is gorgious. Also balanced as its on par with daedric. Mods like that really make me wich i didn't play on console.. They also make me grumble at a friend of mine who simply insists on showing me screen shots of the latest mod she's trying out.