Dump CTRA; Switch raid mods. Get oRA or something similar; that will give you MT windows and targets. Then get some raid frames to pair it with; SRaidFrames, Grid, agUF, there's a ton out there.

Then get yourself a contextual mod, like Clique, or set up OnMouseOver macros for decursing and such. It's really less complicated than it seems.

You should outline a few goals for your healers. Get them grouped up into healer channels for communication and get some people that are willing to give healing assignments.

I personally prefer to heal your own group and then where other help might be needed. Often there is some type of group assignment set up for boss encounters where a healer is to only heal a couple of tanks due to the nature of the encounter and healing requirements.

For mods, if you want to be good at healing AND know what your raid is doing - you're going to want some mods that are able to display the entire raid. Try PerfectRaid (recently released as a Beta for WoW 2.0) or perhaps ag Unit Frame' raid windows. Couple this with oRA2 and BigWigs. I'm not sure how CTRA is anymore, but it it is anything like before, for my personal taste the raid windows are too big, which is why I switched to PerfectRaid. More info, easier to read, etc.

With oRA2 you can set up key-bindings for MT's and PT's (I find this to be extremely important as a healer so I can quickly target the MT's of my choosing without using my mouse).

Also, Clique is a good mod for those that use the mouse a lot. Makes for quick dispelling/decursing and even healing if you've got a mouse with more than 2 buttons :-P

[edit] oRA is compatible with CTRA.

Huge thread on UI mods here: http://forums.elitistjerks.com/viewtopic.php?id=9451. Might also want to check out here: http://forums.elitistjerks.com/viewtopic.php?id=9562.

Many options will give you similar results. A common choice is Grid + Clique, and something like oRA + sRaidFrames (although I think that perfectraid is out now, also)

This has been covered, as mentioned above.