Does the Magus's Spellstrike combine strike damage with spell damage?
If I Spellstrike with a slashing weapon and Gouging Claw and an enemy has Resist Slashing 5, Do I subtract the 5 from my damage once or twice?
If my weapon has the Flaming Rune (1d6 fire damage) and I Spellstrike with Produce Flame against an enemy with Weakness Fire 5, do I proc the extra 5 damage once or twice?
Twice. The rules would have to say that the spell and strike are combined for weakness and resistance, since that isn't a default assumption. No rules say that.
You would first need to decide if spellstrike counts as a single instance of damage or multiple. All the damage comes in with one attack so I'd say it's one instance with the rules on weakness.