re 1: Yes. 

Recently the equivalence between the Jacob Lurie's model for [infinity-operads](http://ncatlab.org/nlab/show/(infinity,1)-operad) via "$\infty$-categories of operators" and Ieke Moerdijk's model (together with D.-C. Cisinski based on work of Weiss) in terms of [dendroidal sets](http://ncatlab.org/nlab/show/dendroidal%20set) was established, in

* Gijs Heuts, Vladimir Hinich, Ieke Moerdijk, _The equivalence between Lurie's model and the dendroidal model for infinity-operads_ ([arXiv:1305.3658](http://arxiv.org/abs/1305.3658)) .

Via the previously established equivalences of the [model structure on dendroidal sets](http://ncatlab.org/nlab/show/model%20structure%20on%20dendroidal%20sets) with various other models for homotopy operads, notably its [equivalence to the model structure on simplicial operads](http://ncatlab.org/nlab/show/model+structure+on+dendroidal+sets#RelationToModelStrictureOnSimplicialOperads) this now also shows that Jacob Lurie's definition is equivalent to all these.