how should a landlord deal with Emergencies?
Get to the property asap if it is an emergency.
What defines an emergency?
I don't think a Tenant and a Landlord's opinion of what defines an emergency is too far apart.
A broken toilet seat, sticking door and so on, are generally obvious non-emergency matters. Unless the Tenant is an OCD sufferer.
Anything involving serious risk to life or serious damage to the property
would be a fair 'emergency'
A serious water leak, something like loose handrail on stairs, electrical wires exposed and that sort of thing.
So what is wrong with the rented accomodation?