I have tested this with the Dawnguard Waraxe and they can be enchanted.

I used Paralyze + Magic Damage on mine. I have 100% seen the paralyze effect work. I cannot see the magic damage effect happen however the axe now has a blue-ish glow (as opposed to green for paralyze) indicating that the magic damage effect is present. The axe makes the appropriate "magic one handed weapon" sound when you draw it.

The axe will always read "Does additional damage to Vampires" even after enchanting.

It will lose charges like a normal enchanted weapon.

I assume the "additional damage to vampires" is not an enchantment and thus never goes away. Not tested.

Same thing with crossbows and Dawnguard armor. Weapons in vanilla like this existed as well, just look at Wuuthrad.

Yes but Wuuthrad cannot be smithied up to Legendary damage and have 3 enchantments on it.

Are there only wat hammer and axe?

Unfortuantly yes. More short-sightedness on behalf of Bethesda. Lets create unique weapons for the vampire hunters but to all those who play our games as sword weilders and have put unchangable perks into sword sections of the trees why dont you all go sit on a rusty spike as far as Bethesda's concerned.

I have rediscovered the joy of the war axe with this DLC (I was always using swords before), although to be fair I never put perks into "sword, axe or mace" as I find they're a bit of a waste so the change wasn't big for me. I can understand your disapointment.