you're kind of asking 4 questions in this.
1. yes, you can run dailies as a healer. you don't die to MoP daily mobs, they don't hit very hard,
as most tank specs can attest, it takes foreeeeever to kill daily mobs because of this (~10% damage taken => vengeance => AP buff). without vengeance, tanking is on par with healing dps throughput.
2. healadin's have ... mediocre damage. from memory there's 2 abilities that cause damage, and a wicked 20s cooldown once you run out of HP stacks. i think it's holy shock, and hammer, with 3-4 others that do double duty heal/damage, like glyphed WoG or glyphed judgement/denounce.
3. custom CR's will do different things when in melee combat to singular, CLU/tuanha will, singular will.
4. the TMOPDE routines do work, just be prepared for it to take ... 2-3 hours. anything with AoE farming of mobs (pretty much 2/10 quests have aoe farming of mobs, i.e. tiller/gl/klaxxi/ac/sp/iot/dd) will be enduring.
5. as a healer, if you're grouped, it takes all the grunt work out of it. that's explicitly not a supported feature, just a quality of life improvement, grouped dailies are much faster e.g. golden lotus is <40 minutes, etc. easily 50% of the effort is collection of slowly respawning items, sic.
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