I think it interesting the lenders (mostly F/F) mandate insurance, but not earthquake insurance even when you are close to significant earthquake faults.It is my personal view that if a big enough earthquake hits that it causes significant damage to many homes that it would be declared a disaster and cheap loans and options are likely to be available.It really is a calculated gamble.I have a fairly large umbrella policy.  

Usually adjustments in the tens or twenties will cause concern.

Water causes problems from deterioration to mold.

We don’t know any PMCs to recommend in the area mentioned, but since selecting the wrong PMC is usually more harmful than selecting a bad tenant, you might want to read our series about “How to Screen a PMC Better than a Tenant”:https://www.biggerpockets.com/member-blogs/3094/91877-how-to-screen-a-pmc-better-than-a-tenant-part-1-services-and-processesWe recommend you get management contracts from several PMCs and compare the services they cover and, more importantly, what they each DO NOT cover.

If so, I would notify the rep and then send the tenants an itemized bill including the cause of the repair.

Additionally, are there any conditions of the property that would cause my lender to pull their loan?

On larger multifamily it could potentially cause huge issues so it is nice to learn on smaller deals.

I am assuming an immediate rent increase from 700 to 900 would cause the tenants to simply not pay it. 

The only reason an insurance company would want you to replace all those things is if they are old or the cause of the prior claims.

If it hasn't caused any major problems and does make s*** run uphill, I would monitor and let it be unless you just want to fix it and not have to think about it again.