In terms of Internet Connection & Activation:
The game does in fact call home.But, only the 1st time you launch the game.
It calls home, verifies your game is legit, and downloads a really small activation file to your PC.
It does this in the background, and only 1 time ever, at first launch. After that, no internet connection is required to play.
Also keep in mind, Mass Effect will only allow you to have a set number of activations at any given time. (I can not remember if it is 3 or 5)
So, if you decide to Re-Install Windows, it may be a good idea to De-Authorize your game. This revokes the activation from the PC and gives it back to you to be used on any other machine.
The tool can be found at EA's website. Just Google EA De-Authorization Tool if you ever need it.
As far as the patch goes, its 73MB in size.
It can be found here: Mass Effect Community - Game Information
That link will also let you know what the patch changes.
As soon as you can, I would certainly get it. The vanilla ME can be rather buggy at times.
As for the Configuration tool -- Aside from showing the Game Version as Sygnus has pointed out,
theres some options in there that are not available in the games settings.
For example, I have to use it to change to a 16:9 resolution. In game only offers 4:3 and 16:10.
Theres a few other settings as well however that can only be changed in the Config tool.
This is certainly one of the better RPGs out there IMO
If you've never played it before, try to avoid any spoliers and just explore everything you can. Talk to everyone.
Theres tons of side missions to do etc, and it has a great story line.