No, Apple will not accept a return after such a long time (don't know of any company that would).
If it is faulty, you can get it replaced under warranty with a factory refurbished service unit.
If it is not faulty, you can sell it yourself and buy a new one. Any warranty, or out of warranty exchange will only allow for you to swap it for the exact same model & storage capacity as what you have to turn in.
Probably not. Your best bet would be to sell your device then use the proceeds towards another device. You can sell it yourself via Craigs LIst, ebay, etc. Or there are services online that buy stuff (just research them and be sure you're not using someone that's not good). Many places will also give you store credit when you turn your device back in. In the US, Amazon, Best Buy, Walmart will all give you store credit for your used iDevice. The how much depends on the place and condition of your device.
For example, I got $70 from Best Buy for my 'like new' iPod 4. I could have gotten $150 from Amazon, but then I'd have had to mail it in and wait for them to assess it and mail me the credit.
So shop around and explore and see who offers you the best deal. And, if you go this route, what you get will likely be store credit so be sure to sell it to a place where you can also buy what you want in replacement.
Your only option is to sell the iPad and buy a new one.
Apple Reuse and Recycle Program
How to Sell Your Old iPad http://tinyurl.com/85d69lk
Other sources to sell.
eBay Instant Sell http://instantsale.ebay.com/?search=ipad
Sell and Recycle Used Electronics - Gazelle http://www.gazelle.com/
For instant gratification in selling a used iPhone or iPad, Gazelle’s Gadget Trader, an iOS app, is tough to beat. In seconds it detects the device and reveals how much it is worth in good condition. Tap the Sell This Phone to Gazelle button and the deed is done.
Sell Electronics for Cash - Next Worth http://www.nextworth.com/
Buy My Tronics http://www.buymytronics.com/
Sell Your iPad http://www.sellyourmac.com/mac-product-guides/ipad.html
It is faulty, my ipad continuously goes into recovery mode
You asked if it could be traded for another product. The answer is no. If the device is faulty and under warranty Apple will provide an identical replacement product. No one questioned whether the device was faulty. Your desire to get a different product is not going to happen and that was your original question.