@Thekarens how is it that apps you purchased through apple are available on your Nexus? Doesn't the Nexus run android os?
That is correct. What they meant, was that once they bought their iPhone, all of the apps purchased for the iPad were available to it. There are exceptions such as iPad only apps, but those are increasingly rare from my experience, as most apps are now universal and include the iPhone and iPad versions for a single price. The Nexus 7/9/10 (and nearly every other non-iPad tablet) do run Android, and have a separate app store where things would need to be repurchased. Short of newer iTunes music purchases, nothing will be able to be shared between an iPad and an Android tablet.
As an answer to your original set of questions, the iPad Air 2, will receive support for at least the next three iOS versions as sanke1 said. I'd be surprised if my Air 1, was cut out of that round of updates. The iPad Air 1 and 2 are both incredibly powerful tablets that Apple will have no reason to not support with future OS updates. Eventually, the first generation Air will be left behind because of tech specs (almost guaranteed to be the 1 GB of RAM), but the Air 2 will be supported for quite a while.
In the off chance that you've received some sort of lemon, where the battery dies out on you within the first 2-3 years, I'd except you to have some pretty close to original battery life for the next 3+ years. Apple rates their batteries as holding up to 80% of their charge after 1000 charge cycles. I hope I don't step on anyone's toes or insult your intelligence, but am going to explain what a full charge is. Whether you charge it twice from 50% back to 100%, from 60% to 80% 5 times, or from 0% to 100% once, they all only count as one cycle. Even charging it daily, the battery should still do just fine for the next 4 years. Considering the full capacity is supposed to provide 10 hours of battery life, 8 hours would still be plenty for most people. Apple does have a service where they will replace the battery. At $100 before shipping and possibly tax are figured in, it isn't the cheapest option, but it is much cheaper than a new device. The warranty Apple provides, only covers the battery for the first year. There can be exceptions where extended warranties have been provided for devices, but that has meant that a large quantity of devices were affected, and someone likely won a lawsuit against Apple for such problem. The 2011 MBPs are the first to come to mind, but I know certain models of iPod have had similar experiences.
My family own iPads of various model types, ranging from the iPad 4, iPad Mini, and iPad Air. This all being spread across 2 of my siblings, myself, my mother, aunt, cousin, and grandmother. The iPad 4 was purchased early 2013, the 4 iPad Minis were all late 2013, and the 2 iPad Airs early-mid 2014. No one has made any mention of bad battery life or any noticeable difference, in fact I'd like to give an example using my own Air. For a quite a while, it's general use was roughly 2 hours of YouTube a day and maybe an hour of web browsing, I'd have to charge every 4 days or so. I'd run it from 100% down to around 5%, then plug it in and let it fill up. With that sort of usage, I'd expect to charge my device less than 100 times a year, battery would theoretically hold ~80% of it's battery capacity for 10 years. You won't realistically get that sort of life expectancy from a mobile device, I just did this to show you that the battery will likely outlive your plans for the thing. Apple will stop providing updates way before you need to tether it to the wall to use it.
I do want to warn you, that as your device nears the end of Apple's support, apps are likely to become less optimized and more taxing on it. Currently, I don't believe I know of any apps that actually challenge the Air 2 in terms of processing power or memory usage. If Apple were to release an iPad with a quad-core processor with 3+ GB of RAM, and programmers manage to create something that utilizes all that power, only then will your Air 2 struggle (this is likely to be many years out yet). In the meantime, I hope you can enjoy your new gift, and utilize it in any way that works for you.
Finally, as another example of how long these devices can last, my job gave iPad 2s (Wi-Fi + Cellular) to some of our salesman. Rather than providing them with Laptops and teaching them to set-up tethering on their phones, IT purchased the cellular capable iPad 2s and deployed those. Granted, they aren't playing the latest games on them, but for completing tasks such as accessing Microsoft Office documents, using our web applications, and email, they can't be beat.
tl;dr
You should expect a minimum of 3 years of good usage from your new iPad. It should be able to last quite a bit longer than that, but I wouldn't expect more than 4 years of support from Apple. The battery will likely outlast your interest in continued use of it.