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No, but it is indirectly. If you have more haste you can cast more spells per time and have therefore more Echo of Light. The same is true for crit by the way: EoL can't crit, but when the triggering spell crits, EoL is higher.

On the Tsulong encounter what are you guys healing with in the 5sec bracket after the sun breath? IF+Gheal then 2 flash & 1 or 2 ticks of penance? Is it worthwhile to put a renew in there or is the sun breath buff dynamic and renewing Tsulong would be useless?

I can only recommend you to switching to holy for that encounter, since guardian spirit once per day phase is an enormous hps boost to all healers and holys mastery does net you a benefit while discs does practically nothing.
If you only have a disc specc I'd say precast IF GH while he is casting the breath, penance and flash spam afterwards.
Since renew snapshots your buffs/debuffs it will only be empowered if cast while you have the bathed in light debuff. Therefor renew is not really worth it, maybe if you can't squeez in a flash anymore, you could apply a renew with your last gcd... as holy in serenity chakra you can apply it beforehand and it will get updated once you refresh it via a direct heal.

Holy works pretty well during the night phase, too. PoM bouncing all the time due to the debuff and Coh keeping people up together with things like healing rain etc work quite well. Also shamans will love you for the guardian spirit... our resto shaman did a 3.5mio crit yesterday on the first breath during the first day phase with my GS up thanks to his mastery

Is Atonement healing affected by stacks of Grace?

Do Atonement ticks from Holy Fire update dynamically with crit rating as other DoTs do? Does the healing from those ticks?

Do Atonement heals proc Price of Progress or is it just healing spells like PoM, PoH, Renew, etc?

Does healing done while SS is active proc Price of Progress? I know it's affected by Grace and AA, but is it still considered a "healing spell?"

Atonement Healing is affected by Grace, though you cannot apply it with dealing damage and healing through atonement.

Neither the dot component from HF nor any other DoT for that matter updates dynamically with crit rate. DoTs and HoTs always snapshot the casters current stats (crit, haste, sp, etc) and are only dynamic in regards to the debuffs/buffs the target of the DoT or HoT has.
If you have a Renew on you tank who currently does not have Grace, applying Grace to him will increase the next ticks of Renew whereas gaining a SP procc yourself does not change the value of the already running renew in any way.

I can't really help you with PoP since I don't wear it anymore and was Holy nearly all the time when I did.

Could you provide a link to that?
I would be very puzzled from a programming standpoint why only one of the values would be checked and not the others...
Also testing it seems near impossible with an rng based stat like crit which has to change during a HoT/DoT.

Edit: I'm stupid... I noticed I can just go to the quoted post. Has Hamlet provided any tests or something for that behaviour? This really strikes me as an odd behaviour if crit were to dynamically update...

DoTs/HoTs roll for crits on each tick so why not use the caster's current crit rate instead of maintaining individual crit rates for each DoT/HoT placed by the caster?

I haven't read the whole thread, but to my knowledge he hasn't provided specific proof of this claim. I am only quoting what he wrote. He's been doing druid guides for awhile here on EJ, so he is credible.

Since each spell has a different relation to your current spellpower, it probably makes more sense to assign a damage value to each tick when the spell is applied than it does to re-evaluate the amount based on current spellpower for each tick of each spell. Determining the damage output of a tick of a spell based on a spellpower value is computationally intensive compared to the (X or 2X) decision performed by a crit roll.