The iBooks versions of Hal Leonard Real books is very poor although readable. They were badly produced. Perhaps they used OCR for the titles (there are occasional spelling mistakes in titles and composers so not all the searches would work). I have the Real books volume 1 and 2; perhaps the newer volume scans are better?
There are two views of the chart, one, page size, where the margins are large reducing the size of the notation and the bigger size by tapping the chart so it fills the page but you lose the title (as it only shows the staves and if there are empty staves at the bottom, these are shown as well). If the song is two pages, in big chart mode, you cannot swipe to the next page.
The TOC works and you can search (obviously only within the one volume you are in).
You can read the notation clearly (it is slightly fuzzy but readable).
(iPad Air)
I do not know what happens if you have purchased the Kindle version and how it functions and looks within the Kindle app (nor directly on a Kindle itself).
I hope they produce a better rendering of their publications, or perhaps an app within which you can purchase them, with a global search, playlist function etc.
For exporting, you can do a screenshot (if it is big view, there is no title), and I would think cropping out the margin in the smaller page mode would reduce the resolution and not be as clear in full screen on an iPad. There is no Share for a page if that is what you are wanting, presumably for copyright reasons.