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I'm not clear on the type of Palm that you are referring too, but you may be describing 'pups' on your Palm.
Here is a link with more information.

https://www.gardeningknowhow.com/houseplants/ponytail-palm/propagating-ponytail-palm-pups.htm

There are several major factors to consider when looking to plant a Cabbage Palm:

1. The trunks on Cabbage Palms can get to be 18- to 24-inches wide
2. They can grow to between 40 and 60 feet tall and
3. They need well-drained soil.

Cabbage Palm roots aren't known for being invasive or spreading so much that they cause issues, so you should be able to plant it about 15-20 feet away from the house without causing any problems.

Here is some additional information about growing Cabbage Palms:

https://www.gardeningknowhow.com/ornamental/trees/cabbage-palm/cabbage-palm-care.htm

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

This link will help you.

http://www.palmtreepassion.com/windmill-palm-tree.html#.V1oM3yMrKi4

This is likely a Scale infestation.

Here is an article with more information.

https://www.gardeningknowhow.com/ornamental/trees/sago-palm/white-spots-on-sago.htm

Pruning should be limited to removing yellowing, diseased or damaged fronds. Over pruning can lead to the decline or death of the palm.

https://www.gardeningknowhow.com/edible/fruits/date/date-palm-tree-care.htm

I'm not sure what may have happened with your planter, but pooling water can be quite detrimental to your plant.
I would considered changing out the pot for a new one.