If you don't know, why would a NEW OWNER want to tack it! Treetrimmer for the oversize buttonwood (shade does sell houses vs a/c higher bills). Grass seed and water is cheaper than sod & water (rake in peatmoss into the dirt before seeding).
Kill the $1,000 for the appliance allowance - that is just a flag to buyer to dicker 3 times over that amount. 1st time buyer will try for parents to foot appliance bill as housewarming gifts.
You make very good points. I was actually thinking today of hiring a landscape contractor--someone who would know the local trade market and could get the most out of a small budget.
The tree is not a buttonwood. I thought it was a cottonwood but when I looked online for a picture, I realized I was wrong. It is a type of poplar. Think tall with little to no spread for shade. Planted in rows, these make good windbreaks for farms but a lone specimen in the middle of a small residential yard just looks bizarre. Also, there are other shrubs and trees (arbovitae I think) in random places. One is planted at the corner of the house--just butts right up against the house and the corner edge of the house projects into the tree branches.
The lawn is coming along. It was dead when we moved Dad out of the house last year. I hired a lawn fertilzer company and paid my nephew to water. It is filling in and is green but there are still areas that are more weeds than grass. If given another year of care, it will look very nice. Your suggestion of grass seed reminded me of a few years ago when Dad decided to address his dying lawn. He spread peat moss and grass seed and then we watched as the birds came in and ate the seed. Of course, Dad didn't have the strength to continue hand-watering his lawn and that is why it died. He refused to let us put in a sprinkler system.
Then there is the giant gazebo in the back yard. Right in the middle of the back yard. It is not your typical gazebo. Dad designed it himself and was so, so proud of it. It is a geodesic dome-type structure. It is screened on all sides. He used it as an outdoor bedroom in the summer when it was too hot indoors. He had a tv and lights in it. Of course, the electricity was provided by extension cords coming from the house.

Up until the last weeks of his life he would tell me how wonderful that gazebo was and to make sure I didn't pull it down because someone was sure to love it.
Well, will they? I don't know. I don't. It could be a nice outdoor dining room or a giant play house for somebody's kids.
This is the problem: I don't know what the majority of buyers are going to want or what they are going to notice or not notice. I think alot of it is a gut reaction and not necessarily a definite cognition. Some things just feel right or feel wrong and we may not know why.
This house and property have felt so wrong to me for over 30 years. I'm just relieved that Dad left us enough money to try to remedy it. I've spent some time talking to the next door neighbor who asks me what are you going to do about xxxx" or "what about yyyyy?" It helps to have other people's input.
I really appreciate the advice here on TUG.
Edited to add: And speaking of other people's input, I asked my sister to do a walk through with me so I could have new eyes seeing and evaluting the property. My sister has owned and sold many houses over the decades. She has impeccable taste and can turn junk into treasures. She really has the touch. After walking through the house, she turned to me and said, "I am so sorry. So sorry. This house is uninhabitable. Tear it down. I'm so sorry you have to go through this."