Q1: What is the most effective way to use earthly star on AST? Not to sure even after I read the skill description multiple times. Just want to use this skill effectively.

I throw it out during big pulls, right in the middle of the pile. Helps me to manage my DPS and healing actions (specifically for tank and melee DPS). Plus I have a burst heal if I need it before it auto pops. For bosses same strategy applies.

Q2: How do you deal with people outranging your group heals? In a lot of boss fights with huge arenas or trash fight with huge areas I always have a problem with BLM/SMN not wanting to group up for group heal after party/raid-wide damage goes out. I have been using rescue skill to pull them in to save the poor souls but I have been chewed out for using that skill. In the 63lvl dungeon a lot of BLM especially get mad when I use it to save them from then volcano blasts that follows them because they are still standing in Ley Lines trying to get a spell off. How do I combat these types? Please help, it is becoming tiresome to deal with this.

I've learned to not even bother trying to explain this to the party anymore lol. I just throw out my Aspected Helios and then throw on Aspectic Benefic to whomever I miss if I feel the need (usually just on bosses to be safe). You could use Rescue, but I can easily see that causing more headache than necessary.