Can iPad Air be hooked up to AOC desktop monitor? How? We have older person in home needs larger screen. Thanks.

You will need an adapter. Here's a lightning to VGA cable:

http://store.apple.com/us/product/MD825ZM/A/lightning-to-vga-adapter

Here's a lightning to HDMI cable:

http://store.apple.com/us/product/MD826ZM/A/lightning-digital-av-adapter?fnode=3 a

YYou can connect with the cables listed above or with an Apple TV device. Keep in mind that and ipad is what it is and was made to be used as it is. I can tell you first hand that what you are trying to do will likely not be of assistance since the ipad is still required as the user interface. Connecting to a larger display maybe fine for watching movies if that's what you have in mind but for overall use the ipad will still have to be used and thus looked at to type and touch. Even with a bt keyboard there are still to many limitations That only a mouse can solve along with a keyboard and display.

All said, you may be better off looking into, and perhaps using along with the bigger screen, some of the features that can be found in (general-text size) and (general accessibility) settings. Other then that, if you are not mindset on the ipad experience, there are other products on the market that are better suited and more affordable. I have provided care for my mother in law from here 80's to mid 90's. Been there, done that.

Only you can answer that.

If you think that the Mac Mini will do what she needs, then yes by all means buy her the Mac Mini. Note that the Mac mini runs on OSx yosemite which will be quite different to the iPad's iOS. However she will get the benefit of a mouse and keyboard to interact with it.

The Mac Mini is a desktop computer, and such will not be able to be moved around like the iPad, as it would require lugging the monitor with it, and an electrical outlet.