The insurer wants to inspect my rental. Is that a bad sign?
No, it is routine on non-owner-occupied property and it usually works in your favor. If it produces a list of conditions, fixing them generally secures better terms than you would have been offered otherwise. Refusing the inspection is what causes problems.
The property has been empty for two months. Am I still covered?
Possibly not fully. Most policies restrict cover after a stated vacancy period, commonly sixty consecutive days, and vandalism and water damage are often the first things excluded. Tell us when a property is going to sit empty and we can arrange cover that holds through it.
Why is insuring a rental out here more expensive?
Protection class and distance from the owner are the two biggest factors, alongside the usual construction questions. Both are facts about the address rather than judgments about you, and both are worth confirming rather than assuming, because they also determine who will write it.