Moonfire and Sunfire can only run simultaneously while we are in Celestial Alignment or they happen to be long enough by the 2 sec duration ups from crits that they overlap each other by 1-2 tick. You have Moonfire and that transforms into Sunfire. You can't just apply 2 of them together anytime. (Even in Celestial Alignment you only have Moonfire but casting it applies Sunfire DoT too)
Shooting Stars proc chance is lower (only by a little bit) than it was before, but Starsurge hits harder. However the new chance depends on crit, so actually it can be higher than before if you gear for crit. But haste can increase the chance too due to faster MF ticks. With the modifications to our rotation we have better Nature's Grace uptime. With the new build it seems like we can have 100% uptime on Nature's Grace once we reach 25% haste on our gear (in case we don't stop casting because of interrupts or movement). That means 45% haste in total (25% gear, 5% aura, 15% NG) and about 30 sec for a whole Eclipse cycle from Lunar proc to Lunar proc (or Solar to Solar). This also means 30 sec cd on Starfall since it will reset on every Lunar proc.