Did Renly know about the Stannis/Jon incest investigation/plans? Why didnt Renly bring Stark in on things, since he probably knew and had weeks of time being in the capital with Eddard but does basically nothing till Robert is dead. Or heck why not bring Jon Arryn in on the replace lannisters with tyrells plan?

Renly knew.

Actually, Renly did sort of bring Eddard in on it, rather inadvertently:

Ned was not sure what to make of Renly, with all his friendly ways and easy smiles. A few days past, he had taken Ned aside to show him an exquisite rose gold locklet. Inside was a miniature painted in the vivid Myrish style, of a lovely young girl with doe’s eyes and a cascade of soft brown hair. Renly had seemed anxious to know if the girl reminded him of anyone, and when Ned had no answer but a shrug, he had seemed disappointed. The maid was Loras Tyrell’s sister Margaery, he’d confessed, but there were those who said she looked like Lyanna. “No,” Ned had told him, bemused. Could it be that Lord Renly, who looked so like a young Robert, had conceived a passion for a girl he fancied to be a young Lyanna? That struck him as more than passing queer.

See, here’s the thing about Renly and the investigation: it is not in Renly’s interest for the truth to come out unless and until he’s succeeded in getting Margaery into Robert’s bed. Because if the truth comes out and Robert is unattached, then Stannis becomes the heir to the Iron Throne. 

However, if Robert is remarrying to Margaery, then the Tyrells replace the Lannisters in the King’s Landing power structure but because Renly’s brokered the deal and is romantically attached to Loras, they become allies to his faction. And while Stannis might temporarily be the heir to the Iron Throne, the moment that Margaery becomes pregnant, Stannis is out of the picture and Renly’s path to a Handship/Regency is clear. 

So what’s happening above is that Renly is both trying to get info as to whether the Margaery as Lyanna 2.0 thing will work but also seeing if he and Ned are sympatico, and neither works. It previews Renly’s pitch to Ned, in that he completely misunderstands how to appeal to Ned and win him over.

As to why not Jon Arryn, well A. Jon Arryn suddenly dying kind of makes that impossible, and B. there’s no reason to assume that Jon Arryn would favor Margaery – he might push for some other marriage.