They are the department that records deeds, liens, mortgages, and a lot of other stuff into the "public records".

You start well, but adding a bit more value upfront, such as positioning yourself as someone who "specializes in helping homeowners sell quickly and hassle-free," could increase receptiveness.Asking if they’re "hoping" to sell the house is smart and non-aggressive.

So we had to prove the unit was existing for more than 20 years but providing public records and voter logs and getting neighbors to sign statements.  

In contrast, property tax liens are non-negotiable and must be paid in full to avoid losing the property.

Probate is public, requires paperwork, and changing of the Title/Deeds. 

So my personal take: If you feel like having a non-contingent offer will allow you to be more competitive and save $10k+ on the new home because of a bidding war/multi-offer situation, then it may make sense. 

I've had negative experiences with a bad general contractor and a non-paying renter (leading to an eviction), so I'm being extra cautious in selecting the right lender this time.Could anyone recommend a trustworthy lender in the Los Angeles area who can guide me through this difficult time?

Most will likely stick to the technical limit of Sept 2021 when it ceased being a primary residence, but some may be comfortable going by the address on the 2021 return and others may explore a partial exclusion, depending on the reasons for your move abroad.If you'd like to read up on the technical rules, the IRS publication 523 gets into more detail than most people would like to know, but it does have some helpful tables and examples for different scenarios.

Is there a website that shows this kind of information publicly?

keep in mind documents affecting title are recorded at the county recorders in every county in the US as such they are open to the public.. and anyone can walk in an record documents now certain things need to be done on the documents to record them..