I believe the damage from the earthquake would be bigger caused by aftermath fire than by the earthquake itself. 

I dress professional all the time.

I'm hesitant to pour a ton of self leveling compound due to added weight on the foundation may cause more settling damage. 

Personal Liability: For claims due to Bodily Injury or Property Damage that you Become Liable for and which is covered under the policy.

Should I drive up or fly in after hurricane to assess the damage and do some immediate repair, while wait for contractor available?

Many of the neighboring units were tagged as destroyed and would need to be rebuilt with a further setback from the ocean but we got lucky and our unit was not destroyed but it was heavily damaged. 

It wasn't until we had hired a house inspector to do a routine evaluation that we realized how much damage her pets had done. 

At this point you would change the locks, survey the property for damages and work to be done for rent ready.

most likely laziness or misplaced trust. the only person who you can reasonably expect to care for your property is you, and a strongly written lease is your first line fo defense against damages.

The lease was vague and did not cover what happens if the pole attached to the retail building and satellite damaged the roof (leaks),etc. who would be responsible to fix it.