The bluish fish with the black stripe in the bottom photo is (I am pretty sure) the fish sold as the emperor tetra. The picture is slightly too blurry for me to be 100% sure though. Anyway, two species are actually sold under that name:
Nematobrycon palmeri
Inpaichthys kerri
They are fairly similar, but the former is more purple and the latter more blue. The latter species also has an adipose fin (a tiny fin between the main dorsal and the tail fin). On the former species, the black stripe continues onto the tail fin, whereas on the second species it does not. I therefore believe that the fish you have is Inpaichthys kerri.
Both these species are similar: need soft water, tend to be delicate in hard water and overstocked tanks. Best colours develop in well planted, shady aquaria and especially if blackwater extract or peat is used to 'tint' the water brown. In hard water and brightly illuminated tanks these fish fade in colour somewhat. Basically sociable and a schooling fish, but males will chase each other.
Cheers,
Neale
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