Additionally, when it expires, you still have the full version of Office installed locally, so you can work with files locally just like normal.
That is not correct. I mean yes, technically the software will still be installed but it will be flagging up a notice saying that your subscription cannot be verified and it will lock at some point after that. You wont lose your files but you do lose the software. Subscription model is exactly that - you pay as long as you want to keep using the software.
There's a lot of confusion online for some reason with people confusing Office 365 (which is the payment model) with online storage and even with the free Office Web Apps. Office 365 will come with some online storage but you don't have to use it - it's still the same software as if you purchased it outright.
Office 2013 & 365 is all that's available and I want the forever version of office, but all the reviews I see for Office 2013 are all bad...
Just how bad is Office 2013?
It's really nice. Essentially a polished up and slicker version of 2010. I definitely would not want to go back. It's nice and fast and very capable and easy to use. I've really nothing but praise for the MS Office suite with the exception of Power Point. And even the latter is more because I hate the series of slides format of presentations it fosters rather than any actual implementation.
I've convinced them to make the purchase for a new software license but I'm not sure whether they should get office 2013 (forever) or 365 (lower cost upfront).
Really it's going to depend on them. I pay for a subscription. It means I never have to worry about making a purchase of an upgrade and I can install it on five devices. It will be slightly more expensive in the long-run (assuming I upgrade to newer versions of Office when they're available), but not by much and the multi-device (incl. iPad) and ability to stream Office under my licence to someone else's device in an emergency are all worthwhile features to me.
If I pay $100 for Office 365 Premium (has to have outlook)... is the yearly subscription $100 or is it reduced amount?
There's Office Home and Student for about $10 a month or $99 if you pay for the year. MS have also just released a new version even below that which is Office 365 Personal and is about $7 per month. But that has a few lower benefits such as install on only 1PC and 1 tablet (so you could have it on a Desktop machine and an iPad for example).
Many of the poor reviews regarding Office 2013 was that it would crash a lot... is this still true or have MS patches stabilized this version?
News to me. I don't remember it ever crashing and I've been using it since it was released. Only problem I recall is when synchronization on SkyDrive buggered up and I got multiple copies of some documents with numbers attached (e.g. document-1, document-2...) which was something to do with it not knowing which device had the latest version so it kept both to let me decide. Annoying, but not harmful.