So, I joined the dawnguard but I asked Serena to turn me into a vampire. Now I wonder: Can I use Vampire powers (more then the basic one) in human form? Or just in Vampire Lord form? If so, how and when?

No, vampire lord powers are not usable in human form. You can summon a gargoyle in VL form and turn into a human and the gargoyle will still be there though.