Can I trust Steam-powered games? Is there any unwanted behavior installed with Steam?

Yes, you can trust it. It is non-intrusive and all it does (at minimum) is manage your games and patches for you. Anything else is optional.

Steam has an offline mode, where you can play your games without a connection to Steam, granting you total freedom from Valve's servers.

It doesn't install anything but the software you need (like DirectX and drivers for example) and the games and patches. Nothing you don't want, unless you don't want the game you're installing. The only downside is that these patches are kind of forced on you, even for single-player games. If the developer decides to 'downgrade' the game or make a change you don't like, there's not much you can do about it.

I'm not aware of any 'independent verification', but the DRM Steam is itself is very harmless, you can choose to run Steam in offline mode and there would be absolutely no way for them to pull access to your game, except for the fact you wouldn't get patches. Any other DRM can be chosen to be used by the game itself of course, but that has nothing to do with Steam.

Anyway, the choice to use Steam has already been made by Square Enix. If you don't trust them, why are you installing the game itself?

Can I trust this "Steam" DRM (Digital Rights Management) software platform?

Having used Steam for over 2 years, I can say whole-heartedly: yes. I was initially annoyed that I needed Steam to play a single game: after I got a couple of more games, and added some buddies I game with: it's become invaluable. I enjoy the convenience of "no more CDs/CD-keys", fast downloads, integrated updates ... a lot of games I would have not bought before, I've simply bought because it's that convenient. Also, you may want to investigate the company Valve -- have a look, for example, the amount of support and patching they've done for Team Fortress 2 ... as opposed to say, multi-billion dollar companies like EA for their best-selling Battlefield series. That, alone, I think, marks Valve as a stand-up kind of company. (I think TF2 is a crap game, but give respect where it's due.)

Has anybody done any independent verification on how this platform works? (I'm very leery of any DRM after the Sony BMG CD copy protection scandal. Thank goodness for Mark Russinovich.)

I've heard of no such thing. You may want to search Google for this. Steam definitely has the potential to take your private and confidential information -- just as any other application does.

Does the "Steam" platform install anything particularly nasty or unwanted on my computer?

In my experience, Steam DRM has never surfaced as an issue. However -- do understand that the games you purchase may have additional DRM software that is required for the game to work. For example, the BF games require PunkBuster, Anno 1404 has its own (draconian) DRM software. Be sure to research the game itself, and the type of DRM it uses.

Are your fears unfounded? Largely, I think yes. I've heard of no person who has had issues with Steam DRM.

I don't plan to play online and I don't want anything unnecessary installed on my computer, since I only plan to play single player!

As awesome as Steam may be, it really does suck to be forced to install it and sign up for it just for one game, especially if you're just going to use it for single player. You have my sympathy.

Can I trust this "Steam" DRM (Digital Rights Management) software platform?

Does the "Steam" platform install anything particularly nasty or unwanted on my computer?

You can trust Steam as much as you can trust any other installer, really. The steam installer doesn't have any kind of special privileges of access other installers don't have. The Steam client itself does not require administrator accesses, but there may be services in the background that do.

However, Steam doesn't do things other applications can't do. Exercise normal caution.

Has anybody done any independent verification on how this platform works? (I'm very leery of any DRM after the Sony BMG CD copy protection scandal. Thank goodness for Mark Russinovich.)

The platform is quite popular and widely used, so it is fair to assume its security has been assessed by researchers. I don't have sources on this, but I'm pretty sure that if something had been discovered so far, medias would have picked up on it pretty fast.