If the answer of the istikhara, comes back as “the choice is yours/authority with you”, can one do it again, so that he gets an answer like Good/Bad, for example one doesn’t want to take the decision, and wants Allah (swt) to give him an answer, like yes/no, can he in this situation do it again?

Yes it can be taken again. I recommend you take another one on the “Tark,” meaning not to do it. If it turns out good, it means avoid doing it. If it turns out bad, it means do it and proceed.