What should I be doing in my yard this time of year (winter) in southwestern Oklahoma?
At this time, your garden and lawn are at rest. It is best to simply leave it alone. Pruning/cutting, fertilizing and watering right now can cause the plants to come out of dormancy which can cause them damage.
While you do live in a rather warm area, plants still need a rest period. Consider January and February to be a planning period, where you can reflect on what worked over the past year and plan what you will plant and grow for next year.
I have a new lawn I spent two years trying to grow. I used a lawn service last year and insisted on organics, no pesticide use. It looks good, although it has 50% weeds. I am letting the grass eventually choke out the weeds. Lawn service feeds my lawn every two weeks, and I have to mow once per week (I keep the grass longer at 3 to 3. 5 inches). This lawn service is very expensive-and I'm on a tight budget. Does it need feeding every two weeks?
Really, you only need to fertilize 3-5 times over the course of the spring and summer with a final fertilization in early fall. During the fall and winter, the lawn does not need to be fertilized.
Would like to know if there is a safe grass killer to use around fence lines in yard.
A great organic grass killer is simply boiling water. It will kill any vegetation it comes in contact with without being dangerous to pets or people.
We killed our grass on a hillside so we could replace it with ground cover. Now that the grass is dead, we are wondering if we need to remove all the dead grass, or just dig holes to plant the ground cover.
If the grass is truly dead, you can just plant the ground cover there without removing the grass.
Do you level your lawn prior to rolling it?
This article should help: https://www.gardeningknowhow.com/lawn-care/lgen/how-to-roll-out-a-grass-lawn.htm
How do you determine if sod is ready to be mowed for the first time after installation?
Wait as long as possible before mowing your newly sodded lawn for the first time. Generally, about 6-8 weeks after sodding is sufficient or allow the grass to grow up to 1/3 higher then its normal height before cutting. It is a good idea to let the grass grow at least 3 inches tall; 4 is better. For that first mowing, take just a little off the top and come back 2 or 3 days later and take it down to two inches.
Can you double layer sod (sod on top of first layer of sod)?
The second layer of sod will have a hard time developing roots through the first layer of sod. While it is possible, it will make it more likely the new layer of sod will fail.
You should not place the sod on the old one it's important for the grass to connect soil with roots it causes the dirt.