Owning a little over seven acres in the country taught me good over the last twenty years.
Yes, ask the Realtor for information. But as jerseyj said, start with your municipality to see what your responsibilities are in that community. I'd add that you should check out the local access channel once a week for updates and bulletins.
It's good that you know the garbage and recylcing schedule. I would also suggest looking for information on leaf collection (Dates and times. How are the leaves to be bagged or tarped? Where are they to be placed?)
Something like extermination can actually be taken care of through a preventative plan where the exterminator will come in once a quarter and spray for specific bugs. The legitimate ones will actually come in and set bug traps that will allow them to figure out what actually might be in and around your place before they spray for anything.
B4U mentioned several good practices. I would just say, don't just get any flashlight. Get a couple bright LED flashlights and place them in rooms where you will do most of your living, eating and sleeping.
I'd also suggest making a habit of walking your home, inside and out, and the perimeter of whatever property you may have to look for things that need to be repaired or replaced. I do this once a month. On occasion I get a bit anal about it and even use my camera phone to actually photograph what needs to be repaired so I can show it to the person I deal with at the local home improvement center.
My "walk" starts in the attic, checking the rafters and joists as well as the insulation for any dampness or water stains. In all the rooms, I check for any structural cracks in the ceilings and walls. I'll test the smoke alarm in each room. I look at the outlets in each room to make sure there are no burn marks. I'll also check the light switches to make sure they are firm, but not too tight nor too loose. In the the bathrooms I look for leaks both in and around the toilets and sinks. I'll check the shower heads and the drains for clogs. In the laundry I'll check for leaks from the washer and I'll clean out the lint trap by the dryer. I can't tell you how many people wind up with their dryers burning out because they let the lint build up in the exhaust until they could knit sweaters for a small village. In the HVAC room, I'll replace the air filters each quarter. I'll also check the hot water heater for leaks. I have an alarm system and I have it tested remotely once a quarter.
On the outside, I look at the siding for any buckling. I look at the eaves and the gutters for any birds' nests and clogs. If you have vents leading from any of the bathrooms or from your range hood, see to it that you get the vent covers to stop birds and rodents from getting in. Look for cracks in the foundation and any unusual depressions close to the house. It may just be settling, but you need to make sure there isn't something else going on like rotting debris that may have been landfilled in the area. Check any outdoor plugs and spigots to make sure they are in working order.
If you have any property associated with the home, look to see what is on it. Check any fencing to make sure it is secure. If it is chain-link, check for any rust, loose sections where animals may be able to get through or small children. If it's a split-rail or wooden pen-type fence, check the wood for any rot or weak boards.
Make sure you know where your property lines are, especially if you
don't have fencing so you can be aware of what is your property. If you don't know, do not rely solely on a map given to you by the realtor or by the county clerk. It's cost some coin, but in the long run it'll be worth it; get a reputable surveyor in to confirm what is listed in the county clerk's office. If possible, walk the property with him/her so you know exactly where the pins are and any witness features likes trees or boulders.
In terms of energy saving tips, the first one may be the most obvious, but it is usually overlooked. Make sure the thermostat(s) for your HVAC system is/are accurately registering the temperature in the room where it/they are located. Second, make sure the condenser outside is clear of any debris around the fins and the slats. Third, if your heating system is forced air, make sure the coils or natural gas jets are clear and can heat or fire relatively quickly (usually no more than thirty second should pass between the time the system turns on and the coils or igniter have started. Fourth, when you are active in the home, keep the temperature to 72 or 74. At night in the winter, I usually drop the temperature down to 68 and throw an extra blanket on. In the summer, I try to sleep with the windows open unless it is too humid or just too hot. Even then I'll keep the temperature at about 76. Summer and Fall, you can usually do without the A/C and heat and rely on the windows.
Another consideration would be look at LED light bulbs as opposed to the CFLs and incandescents. You can get some info from
this company. I don't work for them, but I appreciate their straight-forward approach.
Hope this helps.