Post whatever form of pay or quit notice is required in your state.  

Sounds like maybe the lot sale was never recorded maybe, your grandfather is still listed as the owner, and the estate is receiving notice if the tax auction. 

If you are parking an RV in your yard, expect a notice to get posted. 

If you have a tax deed, you will need to give notice to vacate, and a little bit of time to comply--maybe 10 days.

I was researching how to calculate depreciation on my first duplex that I bought and I was browsing through the county assessor website and noticed that my land value is $250k and the improvement value is $28k.

It eventually went to auction and when I started poking around at Auction.com I noticed it listed and that it previously went under contract at $165K and was back active again for some reason at $140K with 4 days to go.

For example, there's a famous case where an appellate court ruled that Act 6 Notice requirements apply to Installment Land Contracts.

I just noticed this today.

Have any of the Florida realtors notice a slow down in the past month? 

I would run risk of “serving notice” to someone that is not actually living in my property.