There is no issue using the 5DmkII or indeed your 350D with Zoombrowser under Windows 7 (or 8 etc for that matter). You just download the appropriate version of Zoombrowser from the Canon website - whatever is the latest version for your current operating system is backwards compatible all the way back to the original G1 and D30. You don't need to keep a Vista PC just for your 350D, nor do you need to stick with Windows - there are solutions for MAC OS and Linux too.
While Zoombrowser is perfectly OK for downloading your images, you don't actually need any software to get images off the card (via a reader) or from the camera (via cable), just use the facilities already in Windows, the only downside is you would lose automatic rotation of images.
As pointed out above the other issue is processing your images. If you want to use RAW, you can use Photoshop (£££) or Elements (about £30), do make sure you have the appropriate version of Adobe Camera Raw for your camera - or use DPP (provided free with the camera or downloadable from Canon). Alternatively, Lightroom (about £100) does all these things - downloading, processing and much of what you can do in Photoshop but has a rather different way of working. If budget is a problem, you can use GIMP which is open source, free software that does much of what Photoshop does, but will not handle RAW - you will need to use DPP in that case. You may be able to educational prices for Adobe software by using your kids' names (providing they survive the experiments).
Don't get hung up on this. The 5Dmk2 is a superb camera that can produce images of the highest quality. Its jpeg output is very good. RAW output is even better but there is a learning curve to that. Plenty of advice on this forum - and in the post-processing & printing forum.
16Gb CF cards are fine in the 5DmkII, and your 50/1.4 is an ideal lens - equivalent to L quality - you will now be using all its glass! Remember it will be a wider, "standard" lens on your 5DmkII whereas it was effectively a longer, "portrait" lens on the 350D.