Android - Ad blocking without rooting, OR low-risk rooting
Answering your first and main question: Ad blocking without rooting
On non-rooted devices running Android 4.1.2, 4.2.1 and higher, Adblock Plus will filter all WiFi traffic, but it needs to be configured as a proxy server manually. Detailed instructions are provided by Adblock Plus for not experienced users.
https://adblockplus.org/android-about
Avoid making multiple questions in one single post, make a single one for each single question.
It would be better if you split your question into three individual questions, but since they are linked to each other, I'll answer them here for you.
1) How are 'recovery' firmwares different from ones just called 'Kernel' or 'ROM'?
They refer to different things altogether.
Recovery :
Recovery refers to the dedicated, bootable partition that has the recovery console installed. A combination of key presses (usually power + volume up) or instructions from a command line, will boot your phone to recovery, where you can find tools to help repair (recover) your installation, install official OS updates and/or custom ROMs and other stuff.
Recovery firmwares contain a custom recovery file that enables you to do a lot more additional things than what the stock recovery offers. This can include options to re-root your device, a file browser to browse through your files, format individual partitions and more.
Kernel :
Kernel is the core of the operating system that handles requests to and from the hardware, memory and process management and all the low-level stuff that is necessary for Android to be able to run. It is based on the Linux kernel with a few modifications to suit it to Android versions.
Kernel firmwares contain a kernel that, when installed, replaces the existing kernel and modifies the low level stuff in order to tweak the software to make better use of the hardware. Better battery life, higher performance, increased signal reception, etc. are some things a custom kernel can do.
ROM :
A custom ROM replaces your device's Android operating system — normally stored in read-only memory — with a new or modified version of the Android operating system. A popular custom ROM is CyanogenMod, which gives you a host of new options as compared to the original firmware.
ROMs may contain a different Android system altogether or might also include a kernel and/or a recovery. It's best to read the OP on those threads to find out what it contains.
2) In what way does each of those ROMs differ from the CyanogenMod, which I've happily used in the past but for which there is no S7 Edge version released from what I can see? Incidentally, I used Odin to install CyanogenMod on my old phones, rather than a 'recovery'.
This is subjective to the ROM you are referring to. Some ROMs use the RRO-Layers engine for theming, while others use the CyanogenMod theme engine. Some ROMs might have additional features over those present in CyanogenMod, others might have a different user interface altogether.
As to the unavailability of an S7 Edge version of CyanogenMod, this is because official builds aren't made yet or are in the works.
3) Are there major differences in how the S7 Edge will operate with such a rooted firmware/ROM as compared to the stock one? Specifically, will it be any more vulnerable to exploits etc, given that no-one can really tell whether these ROMs have e.g. built-in trojans?
Again, these are subjective to the ROM you choose. Basically, some offer better performance, others offer better battery life, and a few more offer a mix of the two. It depends on which ROM you choose.
There are a few ROMs that might be more vulnerable to exploits than others. Therefore, it is recommended to go for an official build of a popular custom ROM, as they are tested and checked so that they would not contain malware.
Given all these concerns about Android rooting, is there any way that ad-blocking can be performed without rooting?
As @xangua said, Adblock Plus will filter WiFi traffic, but needs a proxy server configuration.
If not, what is the least-intrusive and least-risky way to root an Android (in this case an S7 Edge)?
Rooting is device-specific. There are different ways to achieve root access on different devices. In the case of an S7 Edge, you could try Kingo Root, it has been claimed to work on an S7 Edge. However, be careful, one wrong step can brick your device.
I have no idea why anybody has not mentioned "Lucky Patcher" yet...
Lucky Patcher is an application that can modify applications/APK files present on the phone by patching them.
One of the things it can do, for example, is remove ads. It's ad removing mechanism is very powerful and can not only make ads not load, but also remove/shrink the ad boxes so you wouldn't even think they were there.
It needs root if you want to patch applications without reinstalling them but it can also patch applications without root by uninstalling them, patching them and then installing them again.
It can do many other things too (some which are illicit and I highly discourage you from doing them)...
The application's interface can be overwhelming and takes some getting use to but once you get the hang of it, you will find it's power beats almost every other adblocker for Android out there.
How to patch an application to remove ads:
- Open Lucky Patcher and tap on the application you wish to block the ads in.
- Tap on "Open Menu of Patches"
- Tap on "Create Modified APK File"
- Tap on "APK without Google Ads"
- Customize the ad-removal settings (if you want)
- Tap on "Rebuild The App"
- Wait until the patching process is complete and tap: "Go to file"
- Tap on the first item that is in the list that appears
- Tap "Uninstall and install" and follow Android's uninstall and install dialogs
- Open the app and confirm that the ads have been removed!
Lucky Patcher can be downloaded here.