When making a healer, is it better to focus on power or crit in early/mid/late games? Can someone provide some concrete examples with numbers on which is better in what situations?
All three healing trees have some amount of synergy with Crit, and will want to achieve at least some baseline amount.
I've tried to use spell and talent names interchangably, often alternating between Republic and Empire talent names for the same effect. I always use both together the first time, and will generally alternate thereafter.
Mercenary/Commando healers (Bodyguard or Combat Medic trees), will probably want to get to get enough crit to keep Critical Reaction/First Responder up as much as possible. This is a 5% Alacrity (haste) bonus that lasts for 6 seconds after a critical heal. Since most heals for this spec are Instant or 1.5 seconds to cast, and the lone exception is a 2 second cast. That means that you'll want somewhere in the range of 25-33% crit to have an average uptime of 100%, and probably a bit more than that for it to be a sure thing. This is the only class for whom Crit is purely a throughput stat.
Operative/Scoundrel healers (Medicine or Sawbones trees), get 2 Energy back from Diagnostic Scan crits thanks to the Patient Studies talent. Given the 'gated regen' model and HoT centric healing style of this class, DS is the primary 'filler' heal, and is used to fill free GCD's, and is an important piece of the regen puzzle that makes Operative healing work. Scoundrels also have substantial bonuses to Critical Healing further up the tree, making Crit a pretty desirable stat.
Sorcerer/Sage healers have the Force Surge or Resplendence talent respectively. This causes critical ticks of Innervate/Healing Trance to allow you to use Noble Sacrifice or Consumption for free. Both spells tick 4 times, and when used under the effects of Force Bending/Conveyance, a Sage will have a bonus +25% chance for each tick to crit. A decent baseline of crit from gear will minimize the frequency with which you find yourself casting Healing Trance without a Consumption proc. This is important, because Noble Sacrifice is the Sage's primary regen mechanic - being able to use it without a health penalty or regen penalty is critical to keeping your force pool full and having enough longevity to make it through the fight.
One thing to keep in mind in all of this is that you will always prefer your 'primary' stat (Aim, Cunning, or Willpower respectively) over either Crit or Power, as it provides both. Furthermore, you may well find, especially in the case of the Sorcerer that just this crit is 'enough' for you. Additionally, it's important to maintain a balance between Crit and Surge, as each of those stats make the other stronger. Surge increases the critical effect bonus of your spells. An important thing to note about healing in TOR is that unlike most MMO's, there is no stat that directly effects the size of any healers resource pool, or the rate at which it regenerates. The only stats available are 'throughput stats' that happen to function in a variety of ways. Alacrity allows you to heal more often, but at a cost to your resource efficiency. Crit allows your heals to provide much more throughput, but at a cost of predictability. Power provides less risk, but also less reward - consistent increased throughput and predictability. Another key consideration is that because of the resource model in TOR, all three healing classes rely heavily on HoTs, and in the case of the Trooper and Agent, on a 'filler' heal that has no resource cost, for which Crit is obviously very beneficial.
At the end of the day, healing is as much about style as it is about math, and different players are willing to accept varying amounts of 'randomness' in their playstyle. Adding additional crit will increase the variance in your healings effectiveness, while decreasing the variance in your regen for Sages and Operatives, and speed for Commandos.
I haven't played healer in swtor, but speaking of experience from other games crit is not a desirable stat for a healer unless a critical heal results in a bonus of some kind (other than extra healing). The reason for this is that you want to be able to predict your healing out put so that you don't over heal and so you don't put faith in the randomness of crits
Depends on the class and the skill tree you choose. Some skill trees and options expand on your crits. Some classes even depend on crits to do the real healing so you're better off adding crit instead of power. But you need to analyze the skill trees you're using to see if they depend on criticals or not.
I've played Scoundrel and Consular to high levels, and if I remember correctly, the scoundrel depended more on criticals than the consular, but it might have been because of the skill path I chose.
Do the math - In SWTOR:
+1 Primary skill -> 0.14 HP per heal +1 Power -> 0.17 HP per heal +1 Crit -> 0.017% better chance to crit
How convert this into HP? Consider the HP of your heals! Assume 70% surge +1 Crit results statistically into
500HP heal: + 0.06 HP 1000HP heal: + 0.12 HP 2000HP heal: + 0.24 HP 4000HP heal: + 0.47 HP
Now it's easy to decide when crit is a must have.
In 4.0, Crit is always better than Power. This is because Surge was merged into Crit, meaning that 1 point of Crit increases both your chance to do more damage as well as the actual amount of extra damage that is done. Point for point, it contributes far more on average than Power does (even in the best gear currently available, when Crit is deeper into its diminishing returns).
Please see this forum post for exact stat recommendations, as well as the mathematics and methodolgy behind them.