How to replace Cyanogenmod dialer/contacts/messaging(texting) apps? I have a Samsung Galaxy S3 with Verizon. I've recently rooted it and installed Cyanogenmod 10.1.

Of ocurse, when you buy the phone brand new, it comes with all the built-in apps from the manufacturer. With the Samsung Galaxy S3, I prefer their original dialer/contacts/messaging apps vs. the ones that comes with Cyanogenmod.

Is there anyway to get back the original dialer/contacts/messaging apps and replace the ones on Cyanogenmod? Is there anyway to change custom ROMs to your liking? Is there a apk of the original dialer/contacts/messaging S3 apps?

I'm new to the world of custom ROMs and rooting Android, so please, if you could, be specific and detailed as, most likely, I won't know where your coming from.

Thanks!
The problem with most manufacturer specific apps is that they are tied very closely with their specific framework, and will not work on "vanilla" Android OS.

In your example, Samsung's Contacts app relies heavily on features of their TouchWiz UI that ships standard with Galasy SIII, and will not function properly (or perhaps even at all) on custom ROMs that are not based on Samsung firmware.  CyanogenMod is based on AOSP (Android Open Source Project) and none of the TouchWiz apps will work there.  The same holds true for most other manufacturers' apps that ship with their proprietary UI overlays, such as Motorola's BLUR (or whatever they renamed it to,) or HTC's Sense for example.

Even if you manage to find an APK for a given app, installing it onto a system that doesn't have the required framework could potentially cause issues ranging anywhere from force-closes, to even not being able to boot the device.  Always have a backup of your device before attempting any such modifications and/or installations, so that you can restore your device to a working condition should something go wrong.

As an alternative, you can try and find a 3rd-party replacement app that mimics the functionality of a manufacturer-specific app you're interested in.  In most cases, Android will allow you to set the downloaded app as a default instead of the built-in app.  For example, there are a myriad replacement Contacts management, Dialer, and Texting apps available in Google Play Store (both free and paid varieties.)  I'm sure some of those will have features that you like from Samsung's corresponding app.