Did Renly’s plan for Margaery have a contingency for Robert not actually being interested in her? He never actually took on a formal mistress with Cersei, so why would he now? Maybe he was still still pissed at the Tyrells for their supporting Aerys and didn’t want to hop into bed with one? Maybe he was put off by her young age, since he seemed to like fully grown women? Or maybe comparing her to Lyanna dredged up painful memories and put him off? Renly hinged a lot on something quite uncertain.

Political conspiracy by its very nature involves risk, but Renly took every opportunity to manage his risks. The Lyanna thing was one of them.

However, to tackle your questions:

1. I don’t think the plan was to have Margaery be his “mistress en titre,” any more than that was the plan of the Boleyns or the Seymours. Rather, I think the plan was to pop Margaery in Robert’s bed and then immediately push marriage. 
2. The famously forgiving Robert, who wishes that Loras Tyrell was his son? No, anger from the Rebellion isn’t a factor for that particular Baratheon brother in the same way that it is for Stannis.
3. The age of Barra’s mother suggests otherwise. 
4. Given that Robert’s major drive in AGOT is all about trying to recapture his lost youth, that doesn’t strike me as likely.