It is sago palm. I suggest you when you rinse your coffee press use coffee grounds for watering this nice palm to protect from scale.

Ohhhhhhh sorry, you meant by the corner plant. It is Split Leaf Philodendron Selloum. It is low maintenance plant.

I believe the plant in your last picture (by the fence) is Fatsia.

http://www.ecrater.com/p/13404103/japanese-aralia-fatsia-japonica-20-seeds?gps=1&id=112511193139

Was trying to figure which plant you were asking about. Was this the one you wanted to identify?

It looks like a split leaf/cut leaf philodendron.

I was focused on the sago, too. We had them at a previous home here in Southern CA. They can be pricey which has always surprised me. They're just palms and fairly slow growing which is a good thing IMO. The other plant does look like some type of philodendron. Easy to grow, for sure.

Opps, the one by fence is the cut leaf philodendron. When you said fence, I thought you meant that little white fence thing in front. I would pull that out btw. With some trimming and clean up things look pretty good. The grass is the worst. I might think about putting zoysia grass in and do a sprinkler system to sustain it. You might be able to restore and recover this but it will take several years to get looking good. Some stone in expanded beds would add interest and texture. Perhaps some lava black ones. Not sure what's available in your area.

Corner plant is a Philodendron. Sago Palm in the front can get huge; it will have babies around the base that will need to be removed. Highly poisonous to children and pets. I had a double one in my back yard and had it removed. Leaves and seeds land on the fronds and it is messy to clean.

Looks like you have two more under the tall tree on the other side of the yard.

Sago Palms are also prickly and are bad Feng Shui so I would remove them as well. They are quite demanding and dictatorial in yards. With the size of your home, smaller more compact looks will be better. I would enlarge the driveway side bed and pull out a larger round area and plant an ornamental tree there for curbside interest. Not sure what would work well in your area, possibly a weeping mulberry. They can be shaped and trimmed into interesting shapes and become quite interesting. Here is photo of one.

I would also limb up the tree to right front corner so no limbs are on roof. If you are close enough to coast and hurricanes are potential, I would remove that tree. Too risky to be blown over onto house. Also too close to foundation. Then create a nice bed further away from house with a new tree if you wish.

Your sago palm gives a structural interest to your garden , I would work with it, remove white fence and plant formally, restrict planting to a few species only as this will add a design element , check out Peter Fudge for inspiration.

What I notice is that the former owner had strange ideas about landscaping. The foundation bed is very shallow and plants are not meant to be that close to the house. I would make that bed deeper and bring the plants forward at least a foot.

In spite of the narrow foundation bed the bed along the drive is wide and messy looking. I would remove that bed entirely. It is detracting from the home and really does not give the look of a manicured yard.

It would help if you could get wider shutters. Red door is very nice.