Let's say you have a shared webhosting package with 100MB of diskspace. If a client would upload just 25 pictures taken with a digital camera (3MB on average), you've ran almost out of diskspace.

Is it possible to have images uploaded to assets to be resized automatically to let's say 800px x 600px and thus a much smaller filesize?

You'd have to do some hacking to the code. SS does resize the images, but always keeps an original in tact for future use.

Yes you can do this, al you have to do it to customize your CMS to which well suites your needs.

The silverstripe's GD class provides a lot of methods, read through this
http://doc.silverstripe.com/doku.php?id=gd