If I take the optional Throwing axes by the Dwarf Captain of Khazad-Dûm, can I still use my standard axe for melee fight?
Or must I choose each turn or I will use it as a melee weapon or as a throwing/ shooting weapon?

Throwing weapons are additional to a model's normal weapon, so generally speaking you can throw the throwing weapon at a model as you charge into it, then when you complete the charge (either into that model, or if you killed it, into another model) you can use your normal weapon in melee combat afterwards.

Thanks for the clear answer!