It might be helpful to take pics before excavating.

Black Medic, a member of the clover (legume) family that grows best in compacted soils with low levels of organic matter. Short term controls are spraying with plant poisons while long term control is achieved by correcting the soil conditions that it likes to grow in. Start with a soil test for soil pH and major nutrient levels and then dig in with these simple soil tests to see what else needs be done. 1) Soil test for organic material. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top. 2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains’ too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up. 3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart. 4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell, to a point. Too much organic matter can be bad as well. 5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

OK, macranthos, I broke a leaf. It does bleed a small amount of white sap that looks like it comes from two "tubes" on either side of the main stem. And looking at how the leaves are developing now, I'm less adamant about it being ground hugging. Ground hogging, but it may not always be hugging.

Sorry, palms are definitely not my area :-( A wild guess would be Washingtonia filifera .... I would suggest you start a new post for each plant you need an id for. People often skip long posts because they don't know there are new plants appearing. It looks from a brief skim as if a whole thread is about the first plant asked about. But keep them coming. It's a slow time on the Forum. The succulent in the sand is Carpobrotus edulis. Invasive in Europe, even as far as Cornwall.