Can a witch's familiar learn 2nd level spells even if the witch can only cast 1st level spells?
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Yes to both.
Below are the rules about adding new spells to spellbooks/familiars. Neither version require the spellcaster to be able to cast the spell. You only need to make the spellcraft check.
Arcane Magical Writings
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To decipher an arcane magical writing (such as a single spell in another's spellbook or on a scroll), a character must make a Spellcraft check (DC 20 + the spell's level). If the skill check fails, the character cannot attempt to read that particular spell again until the next day. A read magic spell automatically deciphers magical writing without a skill check. If the person who created the magical writing is on hand to help the reader, success is also automatic.....
Spells Copied from Another's Spellbook or a Scroll: A wizard can also add a spell to his book whenever he encounters one on a magic scroll or in another wizard's spellbook. No matter what the spell's source, the wizard must first decipher the magical writing (see Arcane Magical Writings). Next, he must spend 1 hour studying the spell. At the end of the hour, he must make a Spellcraft check (DC 15 + spell's level). A wizard who has specialized in a school of spells gains a +2 bonus on the Spellcraft check if the new spell is from his specialty school. If the check succeeds, the wizard understands the spell and can copy it into his spellbook (see Writing a New Spell into a Spellbook). The process leaves a spellbook that was copied from unharmed, but a spell successfully copied from a magic scroll disappears from the parchment.
If the check fails, the wizard cannot understand or copy the spell. He cannot attempt to learn or copy that spell again until one week has passed. If the spell was from a scroll, a failed Spellcraft check does not cause the spell to vanish.
In most cases, wizards charge a fee for the privilege of copying spells from their spellbooks. This fee is usually equal to half the cost to write the spell into a spellbook (see Writing a New Spell into a Spellbook). Rare and unique spells might cost significantly more.
Witch's Familiar
Adding Spells to a Witch's FamiliarWitches can add new spells to their familiars through several methods. A witch can only add spells to her familiar if those spells belong to the witch's spell list.
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Familiar Teaching Familiar: A witch's familiar can learn spells from another witch's familiar. To accomplish this, the familiars must spend one hour per level of the spell being taught in communion with one another. At the end of this time, the witch whose familiar is learning a spell must make a Spellcraft check (DC 15 + spell level). If the check succeeds, the familiar has learned the spell and the witch may utilize it the next time she prepares spells. If the check fails, the familiar has failed to learn the spell and cannot try to learn that spell again until the witch has gained another rank in Spellcraft. Most witches require a spell of equal or greater level in return for this service. If a familiar belongs to a witch that has died, it only retains its knowledge of spells for 24 hours, during which time it is possible to coerce or bribe the familiar into teaching its spells to another, subject to GM discretion.Learn from a Scroll: A witch can use a scroll to teach her familiar a new spell. This process takes 1 hour per level of the spell to be learned, during which time the scroll is burned and its ashes used to create a special brew or powder that is consumed by the familiar. This process destroys the scroll. At the end of this time, the witch must make a Spellcraft check (DC 15 + spell level). If the check fails, the process went awry in some way and the spell is not learned, although the scroll is still consumed.