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It sounds like your soil has gotten a bad infection. I would recommend using wettable sulfur to kill off the infection. When you add this, you will also want to add dolomitic lime to keep the pH stable while the sulfur kills off the infection.

I would wait about a month to replant to be sure the infection in gone. The other tree may, or may not already have the infection. It is possible that it can recover without showing symptoms, but it is more likely to share the same fate.

Treat the area as I described, and you will be able to plant again within a month or so.

This does look like frizzle top to me. Here is some information about frizzle top:
https://www.gardeningknowhow.com/houseplants/palms/frizzle-top-on-palms.htm

In case nutrient supplementation doesn't fix the problem, here is some information on palm diseases:
http://ipm.ucanr.edu/PMG/PESTNOTES/pn74148.html

Those are flower heads! They will not likely produce anything, and you can cut them off at any time.

For many palm species, it is normal for the roots to become exposed above the ground, and it's not a sign that the palm is unhealthy or unstable. It looks unusual, but it's simply the way these palms grow. Please see this article for details:
http://edis.ifas.ufl.edu/ep344

This might be a Bismarck palm. Here is our article about them:
https://www.gardeningknowhow.com/ornamental/trees/bismarck-palm/growing-bismarck-palms.htm

Please see this article for fertilizer info:
http://edis.ifas.ufl.edu/ep261

It is best to leave fronds on the tree if they're still green at all. If the frond has turned completely yellow or brown, then you can remove it (or just wait for it to fall on its own).

The only thing you can do here is flush the soil out with plenty of water. Citric acid can help flush it out as well, but make sure to use plenty of plain water after. This will get all of the citric acid out.