To the first part of the question. Erase is not considered damage to the item because it doesn't do HP damage. Physical violence is not done to the book at any point during a casting of Erase.
If I stab the book, throw it in a fire, or otherwise physically harm it, it takes hit point damage like any other object.
Pathfinder doesn't model the theoretical loss of information in the spellbook well because that's actually handled as a sort of damage to a character. The spellbook is a record of character progression in a way. A wizard or alchemist whose formula/spellbook is damaged in the way you've described loses access to those spells if they didn't have them prepared. However, a wizard or similar caster could rescribe prepared spells, as mentioned here
Replacing and Copying Spellbooks
A wizard can use the procedure for learning a spell to reconstruct a
lost spellbook. If he already has a particular spell prepared, he can
write it directly into a new book at the same cost required to write a
spell into a spellbook. The process wipes the prepared spell from his
mind, just as casting it would. If he does not have the spell
prepared, he can prepare it from a borrowed spellbook and then write
it into a new book.
Duplicating an existing spellbook uses the same procedure as replacing
it, but the task is much easier. The time requirement and cost per
page are halved.
The good news here is that duplicating the spellbook is easier, and so most of the time a caster who needs a spellbook should spend the time duplicating it, just so they don't lose what amounts to their entire character progression.
Mending, Make Whole and so on typically cover the structural damage to an object, that is the HP of the object, more or less. Those two are the only ones I could find on the Paizo SRD which cover it. So if your spellbook was a jar full of scrolls, and the jar was broken, the scrolls fall out, neither of these spells would return the contents to the jar.
So, [mending] is a cantrip and reads like this.
All of the pieces of an object must be present for this spell to
function. Magic items can be repaired by this spell, but you must have
a caster level equal to or higher than that of the object. Magic items
that are destroyed (at 0 hit points or less) can be repaired with this
spell, but this spell does not restore their magic abilities.
Mending would only let you repair the jar if you had all of the fragments.
My understanding of the spells leads me to believe that mending would allow you to, were you in posession of the ripped pages of your book and it suffered scrapes, and so on (the typical sort of things that a book might suffer really) you could put it back together and it would be none the worse for wear. If those pages were burned, digested or otherwise discorporated, mending isn't going to be able to repair the book at all. It might fix spills and so on, that's probably at the discretion of the GM.
Make whole can fix destroyed magic items (at 0 hit points or less),
and restores the magic properties of the item if your caster level is
at least twice that of the item. Items with charges (such as wands)
and single-use items (such as potions and scrolls) cannot be repaired
in this way.
This looks pretty good but,
This spell functions as mending
Which means we still need all the pieces unless I'm mistaken. Which is why the spell Book Ward exists. Unfortunately it isn't in the Paizo SRD and I'm away from my books at the moment. It does confer acid and fire resistance to an object, which would definetly help keep that "destroying pages" problem.
Long Story short, if you could put your spellbook back together with mundane means, these spells will save you the trouble. Pages would be knit back in as though they were never ripped, the spine would be uncracked, locks and clasps would be reattached, etc.
If you would actually have to replace pages, their contents or the materials that make up the book, these spells likely will not help you, and you're out of luck. Backup your spellbook just like you (should) backup your files.