What's your question? Ask

Unless you are wanting to propagate them, then there is not a reason that they have to stay on the plant. You may remove them if you wish. This will not harm it. This article will give you more information on the care of these: https://www.gardeningknowhow.com/ornamental/trees/foxtail-palm/foxtail-palm-tree.htm

It appears that you are describing an immature flower sheath. The hard covering will open to reveal the flowers, which mature into seeds.
More on foxtail palms: https://www.gardeningknowhow.com/ornamental/trees/foxtail-palm/foxtail-palm-tree.htm

You palm is developing a flower stalk.

https://www.gardeningknowhow.com/ornamental/trees/foxtail-palm/foxtail-palm-tree.htm

This is of concern and should be looked at by a professional Palm Arborist.
The links below may have some information for you on possible diseases.

https://www.naturepest.com/professional-do-it-yourself-pest-control-advice/foxtail-palm-wodyetia-bifurcata-pests-diseases-deficiencies/
http://abovecapricorn.blogspot.com/2009/10/rotten-falling-palms.html
You can also contact your County Extension Office for local help on palms and possible diseases.
https://www.gardeningknowhow.com/extension-search/

Can you include a photo? If there is still any living, green growth, then there is still a chance. If it is all brown, rotted, or easily can be pulled off, then it is likely on its way out, or dead already, unfortunately.

That one will die... It may send up a replacement from the base, but that trunk will die. It will be easiest to wait until it is fully dead to remove. This will keep it from harming the remaining palms.