Most people will only be able to carry what they can sling over their back with a strap, put in pockets, or carry in their hands. How about you go outside the box and make this your carry mechanic until someone actually finds a backpack, this could be interesting...
The idea is to have the same mechanic for things you carry over your shoulder and in your pockets too, basically nothing should go "invisible" and end up inside of you but you should be able to tell where everything is. So either you have keys for your pockets, or you look at your pockets and what's in your pockets get outlined, and you can see what's over your shoulder by looking to the side while standing still etc.
- The inventory space is very limited, since you are limited by the physical capacity of your backpack. Forget about carrying three shields, two full sets of armour and several hundreds of potions. Since the setting is apocalyptic, having to choose wisely what to pick up and what to leave and a very limited space to carry stuff might work, though.
- Browsing the inventory can be difficult. How will the player access an item that's at the bottom of the backpack? I would rather have the game present me an organised list of what stuff I have than having to spend time moving stuff to find that stupid thing again. Browsing through a backpack sounds a lot easier when you have two hands to interact with it than when all you have is a mouse pointer and some keys.
The limited inventory is something I'm going for, if you need to carry more stuff you need to find a way of doing so, like finding a trolley or something.
Browsing the inventory is the biggest issue to overcome, I'm not quite sure how to do this yet, my main idea (with the backpack) was that you would divide the backpack into layers so if you want something at the bottom you use the scroll wheel to select which layer you're in and all the layers above that layer become transparent so you can see and select easily. This I imagine would also give some more features to inventory management since you would want to place items you use often at the top and items you use less often at the bottom of the pack.
Else, there is Alone in the dark 5, which happen during some kind of apocalypse. There was also a particular way of handling inventory in Alone in the Dark 5, you didn't have any menu, but rather when "opening the inventory", the character open his jacket and look inside his pockets. Is this the kind of mechanism you are looking for?
The Alone in the Dark inventory is kind of what I'm going for only more extensive and customable, so you choose where to put your things and they don't just automatically end up in one specific pocket.
Regarding the AI question, this is something that will probably be better answered in the Artificial Intelligence subforum. My two cents, though. There's almost always a better way to go than a complex collection of if statements. Take a look at this article about behaviour trees. Mind that there might be better options, my experience when it comes to AI is quite limited.
That article was great, if I combine behavior trees with case based learning somehow I should get an AI that behaves a lot like a human and actually gets better and "in sync" with you over time, so having an AI companion for a long time makes it better meaning you won't see them as disposable since you "trained" it. If done correctly I wouldn't have to hard code things like "Trust" since it would be a side effect of it learning the players behavior and what to expect from the player :) Now I just got to figure out a good way to combine the two, but hopefully someone else has already done something similar. Off to more research, thank you :)