Do things on the stack or state-based effects resolve between first strike and normal combat damage?
You're right about #1 in the first case, and #2 is correct in the second place.
If any creatures have first or double strike, there are two combat damage steps. From the comprehensive rules about what happens within every combat damage step:

510.3. Third, any abilities that triggered on damage being assigned or dealt go on the stack. (See rule 603, &quot;Handling Triggered Abilities.&quot;)
510.4. Fourth, the active player gets priority. Players may cast spells and activate abilities.

To end 510.4, both players must pass priority until everything on the stack resolves. When the stack is empty, play proceeds to the next step, which will be a second Combat Damage Step (if the first was for first strike) or the End of Combat Step (normally).