1) Yes, they work together just fine. However it will be a fun conversation with your sword.
2) Nothing against ranged spells. Sure.
3) No. Spell combat specifies that it functions as two weapon fighting and your off hand has to be casting a spell. Strictly by RAW, no, but it doesn't seem like a lot to ask of a DM as long as you don't use your offhand for anything else.
That arcana lets you use a wand in your offhand. If you are doing that, you can certainly spellstrike with the spell cast from the wand.
4) No, the target is not an enemy. You cannot spellstrike it. However it grants its own free trip attempt with casting the spell. You can't spellstrike it and gain an extra attack from it, but you can still use it with spell combat and use the free trip provided by the spell. However it won't cause any damage, it is just a trip attempt.
I would definitely ask about #3. Personally I would allow you to use spell combat with a weaponwand at my table, but I would specify that your off hand is unusable for anything else while doing so.
Well I suppose technically, yes, that would work than. I stand corrected on that point, I misremembered the exact wording.
I'll see if I can answer the other questions later tonight.
Blade Tutor's Spirit) It is based on the caster's caster level.
Charge Spells) You can still use spell combat, but if you cast any touch spells than the previous charges you were holding are gone.
Blade Lash) CMB, but yes.
Tattoo) By RAW, no. Tattoos can only be inscribed upon creatures, which the weapon is not. Also they have to occupy a normal magic item slot, and the sword does not have any slots. But again, I don't think it would be an unreasonable thing to house rule.
Blade Tutor's Spirit) It is based on the caster's caster level.
Charge Spells) You can still use spell combat, but if you cast any touch spells than the previous charges you were holding are gone.
Held charges are lost if you cast ANY spell, not just another touch spell. So casting any spell (whether using spell combat or not) will cause you to lose any unused charges on chill touch. So you are allowed to use spell combat in this situation, it just costs you the rest of your chill touch charges.
Ah yes, bbangerter is correct.
You cannot use spell strike with wands. The wand wielder arcana lets you use spell combat with wands but nothing in it lets you then deliver that spell via spell strike. If you are using the weaponwand spell you can use your weapon to improve your to-hit for the spell (that you are delivering via the wand) but that's all, and that's per the weaponwand spell, not from either spell combat or spell strike.
To put it another way, weaponwand essentially lets you decide, on a round by round basis, what is in this hand: my weapon or my wand. It also lets you use your weapon's bonuses to improve your chance to hit with said wand.
Spell Combat lets you, as a full round action, both make a melee attack (or attacks if you have more than one) and cast a spell. The Wand Wielder arcana lets you use a wand instead of one of your own spells when doing spell combat.
Spell Strike lets you deliver a touch spell (that you yourself cast, so not from a wand, not from a scroll, not from a magic item, etc.) via your weapon. You thereby make a trade: it's harder for you to hit because you are targeting AC instead of Touch AC, but if you do hit you get the advantage of also doing your weapon damage. And if you crit with the weapon, you not only do your weapon's crit modifier but also you double the spell damage.
Finally, remember that unless you have a way to get higher Caster level wands, your wand of Shocking Grasp will be CL1 and will deliver only 1d6 damage (ditto with Snowball, Chill Touch etc.).