Fire ants aren’t a Texas thing, they are a Southern thing. They originated from Mobile sometime between 1933 and 1945, and have spread since. At first, freezing ground prevented their invasion, but they have learned to adapt to freezing temperatures and are spreading. Amdro is a commercial insecticide that is effective at killing a particular mound, but as has been mentioned, loss of a particular mound only invites others to invade the territory. By being consistent about treating mounds on your property as soon as you see them, you can pretty much keep them at bay. You can also just learn to leave them alone and be aware when you are around them. Your choice. They are bastards.
I don’t know about crazy ants, I never dealt with them. You’re on your own with those.
HVAC is easy. It is really just AC, or central air. You might have gas heat, which is just a natural gas heater added to the Air Conditioning unit in your attic. You will be using the AC much more than the heat, so you don’t need to do much worrying about the heating (unless you have a heat pump, in which case, the AC and heat are the same). The main thing is to replace the filter every month. You don’t need a high-filtration pollen and pet dander control filter, the cheap ones do just fine (if you need air filtration for allergies, etc…, you will be better off getting a supplemental air filtration unit than to try to use your HVAC unit to do that). It is important to change it monthly, though. It will keep the whole system clean.
If you are renting, don’t worry about the HVAC, it’s your landlord’s problem. If you own, the biggest problem is age. Most compressor units are good for about 20 years. If you look on your outside unit, you should find a manufacturing date. If it won’t cool and the unit is less than 20 years old, it is probably either the capacitor or the condensation fan (assuming the air handler inside is working properly). The capacitors last about 5 to 7 years, so if your unit is less than 20 years old, find out what capacitor it uses and get a replacement. If you how to operate a circuit breaker and a screwdriver, you can replace it and save yourself $150 with a $20 part. Note that a bad capacitor can kill your condensation fan, so it makes sense to pay attention and fix it when it dies.
If your unit is more that 20 years old, unless you are planning on moving soon, it makes more sense to just replace it when it starts giving you problems. You can just replace the component that fails, but you will be chasing problems until you replace the whole thing. The newer units are much more efficient and will do a better job, so it just makes sense. Do not just take the cheapest option when you replace your AC.