You will probably need to run some of these by your GM. I do believe that the common opinion is that you can by default apply arcane pool to natural weapons and you can spell strike with a natural attack. You may notice that the Natural Spell Combat arcana doesn't even mention either of those other abilities, so it isn't necessary for you either way.
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The issue with the Arcane Pool boosting the hair attack is nebulous, as it states a weapon "you are holding". Check with your GM. Mine allowed it but I don't often make use of that feature in regards to the Hair slam attack. I generally make use of it with ranged weapon attacks, like with a crossbow.
The same issue is present for spellstriking, as you are not actually 'wielding' a weapon with your hair. You would need Natural Spell Combat to make use of your slam attack during a spell combat but nothing prevents you from making a single attack (Spellstrike) with your hair after casting the spell, and it is actually preferable to do so as grappling generally limits you to a single standard action a turn. As before, I don't make a habit of doing so with my hair as my BAB isn't actually all that high, even though my grapple CMB is. When you get the chance to start hitting touch AC (15th level with a Accurate Strike arcana), that's when you really lean into it.
The Witch and Magus don't share a lot of spells, unless you pick a patron that grants some (ie, elements gives shocking grasp). Broad Study is generally what I use to make use of other touch spells outside that list.
I do urge a little bit of caution when attempting to play this kind of character. I would not focus on purely grappling and not making use of it as a primary means of attack. It is powerful and effective, but as a full spellcaster, sometimes your best way to help the party is to use your spells and save the hair for when an enemy gets clever and tries to pin you down. That's when you show them you have the Greater Grappler feat and they are the ones that get pinned down.
My planned build for this character had been 14 Witch / 4 Unchained Rogue / 2 Brawler. The martial flexibility from the Brawler came in handy a few times, as did the sneak attack damage from the archetypes I took plus the Rogue levels (Strangler and Snakebite Striker).
Protip: Real fun starts happening if you take Greater Grappler and can maintain your grapple as a move action (and get a free constrict). As you aren't considered grappled while grappling with your hair, you can use your standard action to cast any touch spell and, as you are already touching the enemy with your hair, it autohits.