[Sony Xperia T, TL, TX, V] schaggo:
Kernel (and some ported tools) only, but of course the philosophy behind the thing. Yes.

Theres a couple of ad providers which apps use to display in-app ads. If there's no free version as in freely free, that's the distribution model a dev choses. Either pay and give the dev a compensation, or use the free ad-supported version from where the dev gets compensation. If you're not ok with either of the latter two, then most common ad providers can be blocked by using a modified hosts file, redirecting server requests for known ad-providers servers to the local loop. You need root access to your device to do that though. More on that later.

Rooting your device is not strictly comparable in running your desktop box with root. Yes, it's running (certain) stuff with superuser rights, but that's not exactly the point. Rooting basically means - among other things - obtaining write access to the otherwise user-inaccessible system partitions (/system, /data et al.) and mess around with them. This is needed for certain things a user might wants to do, sneaking in a modified hosts file, for example. I don't know what you'd describe as "tinker" but I guess yes, tinker it is.

It's usually the same as with every other device: basically theres modified stock ROMs or "real" custom ROMs. The first being for example slimmed down ROMs, with "useless" manufacturer or telco provider added junk-/crap-/adware and -services. Then theres "enhanced" stock based ROMs with added or modified stuff. Instead of 5 notification area toggles you can have up to 14, freely modifiable toggles. Or skin and theme the user interface, or use modified kernels with support for additional services or so. And then there's the "real" custom ROMs which you'll find under "Original Android Development". This is user generated code which you'll find in AOSP or Cyanogenmod ROMs. These kind of ROMs do not base on stock code at all, except for the parts which are highly device specific as closed-source device driver blobs etc, but the system as such is completely open source, comparable to how the Linux/Unix universe works. The benefit of such ROMs is usually that they are quite "barebones" and as such perform much better in terms of interface fluidity etc. But you may miss out on cool manufacturer added stuff specifically tailored for the device at hand, if theres no compatible open source alternative. A great example for this is the Samsung Galaxy Note: the S-Pen is supported in Cyanogenmod, but there's cool S-Pen features CM cant offer, you'll only find them in Samsungs stock ROM. You may find a comparable analogy for the Xperia T, or any other device.

There's no detailed changelog for stock firmware updates. This is the case for most if not all manufacturers. Samsung doesn't release a changelog at all, for example. And updates can be a good thing, or a bad thing. A good thing is added functionality, a bad thing is closing an exploit to root the device, for example. You get the idea.

For the device at hand: there's no big differences between .3.195 and 3.223 or even the "old" .1.303 (or so) so in case you want root but not unlock your device, go ahead, you won't lose much especially if you don't know about it ;)

Well, modern mobile operating systems offer a ton of settings to play around with, you'll find [number of users]*[number of features]^(numbers of features) of recommendations regarding best settings. Basically it's always the same: the more you do, the more you try to get out of your device, the higher the energy consumption will be, the shorter your battery time will be. Apply some common sense and you'll find your own best settings. Probably not what you wanted to hear, but, well, that's the way it works :D