Monthly mortgage payment questions - Hazard Insurance and County Taxes

[Jeff L.]

My lender sent me the itemized monthly mortgage payments I'll be making. Along with the principle and interest are two items I had questions about:

1) Hazard Insurance - does this go away once I'm covered by my own landlord insurance policy? Do I have to have this?

2) County Taxes - A monthly payment for this included in the mortgage. Does the lender pay the property taxes for me from what I pay them? I'm confused about this item.