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You have a legitimate concern, but one watering will not likely cause harm to your plants. Repeated watering with high salts content softened water can be detrimental.

Water heavily now to leach the salts as best possible, and then resume with your regular watering program.

https://www.gardeningknowhow.com/ornamental/trees/palms-trees/palm-tree-planting-outdoors.htm

This appears to be sand, rocks, and debris that have blown into the tree. This is normal for an area that has windy conditions or lots of rocks or dust. This can include construction areas or disturbed areas. I would say that it does not pose any threat to the health of the palm.

It is risky to plant another palm in the same site, especially right away. It is safer to plant another type of tree.

https://edis.ifas.ufl.edu/pdffiles/PP/PP10000.pdf

last paragraph:

"We do not know how long you should wait before it is safe to plant another palm in a Ganoderma-infested site. We can say that the time is measured in multiple years, not months, since the fungus is probably capable of living in the soil almost indefinitely"

But if you are determined to plant another palm, you can drench the soil with a biological fungicide twice or three times this year and plant next spring. This is not a sure cure, but is the best way to attempt to suppress the disease without chemical sterilization.
https://www.gardeningknowhow.com/plant-problems/environmental/planting-in-old-spaces.htm

Five or six feet to allow a somewhat full foliar spread, but maybe you can get away with closer if you can accept a one-sided canopy. The trunks don't get that big, nor are the roots very invasive, so you can go closer than with other palms. But I would say three feet at least.

Are you sure that it was fusarium wilt that killed the previous palm, and not lethal yellowing or gandoderma root rot, which could affect your new palm? Christmas palm normally is not susceptible to fusarium, but I would do a soil drench before planting with a biological fungicide to suppress soil borne diseases.

This can be done, but you may need to have professional help if you do not have tools to remove it safely.

Here are some articles that will help:

https://www.gardeningknowhow.com/garden-how-to/projects/removing-existing-plants.htm

https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-kill-a-tree-killing-trees-in-your-garden.htm

https://www.gardeningknowhow.com/ornamental/trees/tgen/tips-for-choosing-an-arborist.htm

https://www.gardeningknowhow.com/extension-search

It is important to let the soil dry out fully down to about 2 inches before watering again. It should never be allowed to sit in drainage water.

I didn't understand what you have in the bottom of the pot, but an African Violet type soil mix is the best for lady palms so you may want to repot in that type of mix.

Here is more care information:

https://www.gardeningknowhow.com/houseplants/lady-palm/growing-lady-palms.htm