Going from WHM to AST is a pretty simple transition early on and I think people have covered the analogous spells well already. At higher levels the classes start to diverge. Around level 60 you'll probably need to practice with the newer skills as they don't really have direct WHM equivalents.
Lightspeed doesn't really help with raw DPS unless you're AoEing with Gravity. AST's single target attacks are either OGCD or cast faster than GCD. I agree with the mobility and heavy healing, though again with healing it doesn't increase raw HPS. LS allows weaving OGCD's between AoE healing and lowers healing cost, so it's more of a long term gain.
Yeah don't be afraid to use the star before it's fully charged. If you do put it down early you can extend Giant Dominance (2nd stage) with Celestial Opposition, but I would only do this if you absolutely need to.Earthly Star works best when it has at least 10s to charge, but if you're new to a fight, it's a decently powerful heal even uncharged. Fully charged and on a 60s CD, it can handle a lot of the raid wide heals - and should. Also adds a bit to your DPS, so don't forget it.
Just want to add, UC has a damage reduction and a regen. Both of these effects persist even after the shield animation is canceled. Using UC optimally usually means that you cancel it before it runs for the full duration. You can also extend its effects with Celestial Opposition.Collective Unconscious is the most powerful AOE regen in the same. Use this and often you won't need any other healing, just let the HoT do it's work. Must be manually interrupted.
Celestial Opposition isn't niche. It's a pretty critical AST skill. Using it to buff cards is good, but I think it's more useful to extend Lightspeed and Lucid Dreaming. Doing this gives you massive amounts of additional MP and healing capacity. Extending Lucid is especially important if you DPS heavily because AST burns quite a bit of MP.Celestial Opposition extends more than cardbuffs. Pretty niche use but - Buffed up an Aspected Benefic on the tank? You can use Time Dilation and Celestial Opposition to make it last a pretty good while. Ideally this would overlap with card buffs - but if RNGsus and you are just having a really bad, you could use this to DPS more, or if a fight has you spend a while out of range of the tank, or similar.
Time Dilation is probably better used to extend buffs on other party members, like tanks, because it can't be used on self.