Tax exemption in Harris

Hi everyone I just bought a new home in Harris county and i wanted to get an idea what the process is like to file for homestead exemption and what are the necessary steps To do so correctly?

Also I received a letter about 2023 tax statement and it says I owe an X amount, is that a separate thing I’d have to pay or is that part of my Mortgage?

I’m still quite new to all this so I want to make sure I do it right