ACROSS. 1A. anag. SEARCH without right = R.5A. double def.6A. cryptic def.8A. reversal of stage = LEG.9A. staff = ROD contained by 2x Europeans = E.
DOWN. 1D. [theatrical] company = CAST + "executive" first = E.2D. is yours truly = AM I + green = GO.3D. insertion of turn = U into polar opposites [south and north] = SN.4D. variant double def.7D. remove last letter from sharp = TART.
Lots of fun! I agree that 2D is especially clever and I got a chuckle out of 6A, though it took me a while. 6D is the only one I still don't get (though I figured out what it had to be) because I don't know how it means "yes, or no...". Also, I haven't seen "abandoned" used to hint an anagram before, but seems like nearly anything can mean anagram! :D
Glad you enjoyed it! Now that you mention it, on reflection I don't find "abandoned" very convincing as an anagram indicator. (It shows up in a few online lists but I think the nounal sense of "abandon," as in recklessness, is lost with a -ed verb ending.)
The "yes and no" in 4D is intended to indicate that the definition is applicable in one sense, but not in another: I'm thinking of golf scoring, where a birdie is one below par, and an eagle is two under.
Thanks for your feedback, it's really helpful and really appreciated.