2. You would heal yourself if the spell was negative energy... But vampiric touch does not state it is a negative energy effect.
It seems at the very least strongly implied that it's negative energy. For one, it's a gift of the undead bloodline. It's got 'vampiric' in the name. Though admittedly yes, it doesn't explicitly say that that's what it is (so it would hypothetically work on undead just as well as any other creature), so if you read that to the letter it's... untyped damage? Is that a thing in Pathfinder? It applied to some things in 3.5, like the eldritch blast.
About being a dhampir, I would caution that people are kinda afraid of undead and exceptionally violent towards them... I hope you have some explanation for that
He's not quite undead. He's just... living-challenged. Possibly a relic of a very disgraceful incident where a vampire managed to sneak into town, serving as a landmark case for tightening up the regulations (for instance, the need to put up an anti-magic field to deter illusionary fuckery). And he's also wildly magical by his very nature. And he looks a lot like
this, maybe a little chubbier.
Really, he's kind of a melting pot of obvious hazards, to the point where I'd assume he's used to getting his house burned down every now and again while he's out on an expedition. That's actually why he started going on expeditions to begin with, most likely, much safer to be in other places when people want to burn your house down. And you get to earn money with which to rebuild your house too.
Also, fixed up the bits to fit level 7. Fewer spells, but hey, at least we're not already approaching late midgame when we start. I take it we get less cash to operate with as well, yes?