Q: How to transfer files from Photos on Mac to a reset iPhone

The software on my iPhone 5s is corrupted, per the Genius Bar employee. She suggested I back up to iTunes, then backup my photos to Photos on my Mac, and then reset the iPhone and set up as a "new" phone. This would remove the corrupted software. My concerns are:

- how can I get the photos from the Photos app on my Mac back to my iPhone?

- how do I copy my "notes" back to the iPhone? It shows that some are backed up to my gmail account, and some to my AOL account.

- will all my contacts copy back to the iPhone when I sync with iTunes?

- what happens to the data in my iPhone apps? Fiitness records, game scores, etc....is that retained within the apps in iTunes and will copy back to my iPhone without losing data?

The Genius Bar employee was able to tell that the system software is corrupted and therefore needs to be reset. My phone randomly crashes and restarts itself.

Thanks for any assistance!