To the first part, Cuirassier and Uhlan units carried sword and pistol (and lance as appropriate), the Dragoons/Reiters had sword and Carbine (although officers carried pistol instead of carbine).
To the second, The piping/facing colour is the only way to determine within the "Prussian" regiments but the Saxons had the Saxony arms in a bursting star on the Czapzka instead of the Prussian eagle.
The southern German forces (Baden, Bavaria & Wurtemburg) did not raise Uhlans.