Thank you so much, everybody, for sharing your insights and knowledge. I called the location as Pensacola, FL, but the property was in Navarre, FL. I thought Pensacola was in the same Santa Rosa County but I now know it's in Escambia County.
I figured out what was making the property tax look like x3 higher without homestead exemption than the the one with it. I simply took what the current owner was paying ($1,100 )for my analysis. Then, when I saw the County tax estimator,
https://srcpa.gov/TaxEstimator, the first box specifically asks for Property Sale Price. The current tax is based on the county's assessment on $115K, but our price was $263K. So, the tax the estimator gave me (without exemption) was $3155. A lot of lessons learned here. So, for the analysis purpose, do you use the current assessed value instead of what you are buying the house for? Also, I am definitely interested in increase for homeowner's insurance in FL as well.