Short answer: can I sync iOS10 device with iTunes in 10.7?

[tenders]

Regardless of what Mac you have the easiest way to get photos from your camera to your iPad is through an SD card reader dongle into the iPad.

In my experience the more robust way is to go from camera to Mac to Dropbox to iPad. But my approach is to have the master set of photos on the Mac, and to consider anything on the iPad to be basically disposable.

I don't do much in the way of music manipulation myself, but I'm pretty sure Dropbox will work for this too although it might be difficult to manipulate the files from Dropbox on the iPad into the standard Music app. Worst case, you might just have to keep a music folder in Dropbox and play stuff from there. There might be third-party apps that are better music players using Dropbox for the music library.

While inconvenient these do not seem to be wild compromises to have to make using a desktop system that is ten years old and predates the existence of the iPhone.

And to PeterBs comment about MacPostFacto, I am pretty sure there is no way you can use it get even close to Mavericks on your Mini.

[RecipeForDisaster]

It's a WiFi only iPad and I need music when I'm not online. That's the biggest problem... I could technically email photos to myself and save them. I do use Dropbox so that would be another option.... I don't see a good solution for offline music, though.

I rarely ever use my desktop anymore which is why it makes little financial sense to spend money on a newer one. What I need to use it for, it still does fine.... other than this which wouldn't have been a problem if I stuck with iOS nine.

[rich in distress]

My best wishes to you,
I encourage you to not feel frustrated, but happy instead. You are reaching the next step in computing, where you find no real need for old computers, and choose instead to reach for the newest paradigm.
I encourage you to take a look into iTunes Match (it's still around, isn't it?... I hope so, because I'm so very into it)...
At any rate, good luck!!