By the rules, no, a witch can only learn spells from a scroll or another witch's familiar.
Can spellbook act like a scroll since spell is written on each page?
Again, by the rules, no. A scroll is a spell completion item--a spellbook just helps a wizard or magus prepare their spells for the day.
So a spellbook would help which caster classes then?
Magus or Wizard only.
Wow only two classes? So the rest of the classes learn spells as they level then or from other familiars?
Wizards and Magi use spellbooks (and scrolls).
Alchemists use a formula book.
Witches learn from scrolls and other witch familiars.
Clerics, Druids, Paladins, and Rangers can prepare any spell on their list.
Bards, Inquisitors, Oracles, Sorcerers, and Summoners only know spells they learn from leveling.
Why are you asking so many questions about spellbooks? What's real question behind all this?
So if they learn spells lets take the witch for example she learns 2 spells when she levels so is that two spells total or two spells for each level spells she can cast?
Two total.
Expect to buy lots of scrolls.
Actually, three classes can benefit from a spell book.
According to this page, Alchemists can learn new formulas from a wizard's spellbook.
Though that doesn't really add to the topic at hand.
Yes, Wizards must either buy lots of scrolls to write the spell into their book, or "find" another wizards spell book.
I also think witches can learn spells by researching them. Though that can be kinda of expensive.
Witches can also learn spells with the Blood Transcription spell from Ultimate Magic.
It's an evil alchemist 2, magus 2, wizard 2, witch 2 spell.
Blood Transcription
School divination [evil]; Level alchemist 2, magus 2, wizard 2, witch 2
Casting Time 1 standard action
Components V, S
Range touch
Target one dead spellcaster
Duration 24 hours
Saving Throw none; Spell Resistance noBy consuming 1 pint of blood from a spellcaster killed within the last 24 hours, you can attempt to learn a spell that spellcaster knew. Select one spell available to the dead spellcaster (this must be a spell on your spell list); you gain the knowledge of this spell for 24 hours. During this time, you may write it down (or teach it to your familiar, if you are a witch) using the normal rules for copying a spell from another source. Once you have learned it, you may prepare the spell normally.
Since it follows the normal rules for copying a spell from another source, I assume for a witch it works like one familiar teaching another familiar a spell. (Since it can't work like learning from a scroll, since the scroll has to be burnt and consumed.)
The downside of blood transcription is that you can only get one spell from the killed character (generally).
It's a great spell for the vampire witch NPC I made for my campaign.
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So a spellbook would help which caster classes then?Magus or Wizard only.
And alchemists. They can read a spellbook and then convert the spell to a formula.
3 classes out of 4 that "memorize" arcane spells.
And witches familiars can learn spell from another witch familiar, either from the familiar of a friendly witch or the captured familiar of a enemy witch.
Witches "learn" spells by feeding the magical scrolls to their familiars or by having familiars teach each other spells. A spellbook isn't really imbued with magic the same way as a scroll. That being said in PFS at least it's possible to pay to have a familiar teach your familiar a spell for the cost of spell transcription just like a wizard.