Yes, start using the ro water right away. Personally, I didn't do a water change in my tank until it was finished cycling. If there is any way to get that sand and lr in the tank now, I would go ahead and do it. It will more than likely cause another cycle in your tank if you wait, therefore making it so much longer until you can start adding the "goodies". It will at least be a mini-cycle, unless you are absolutely positive that both the lr and ls are cured, which is almost impossible to determine, especially with the amount you plan to add. As for the coralline, it will take about 4 to 6 months before you start to see that take off. Your ph looks a tad high, also. But that is a whole other can of worms!!!! Let me know if you want the 411 on that, and I'll see if I can't find Broomer's (my hero) thread on the relationship between alk, ca, and "stuff".
And about the hair algae...just start picking it out if it bothers you.
HTH