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It's best to get your palm planted into the ground.
This link will help you.

https://www.gardeningknowhow.com/ornamental/trees/canary-palm/canary-island-palm-trees.htm

From the photos this appears to be a very extensive amount of decay in the trunk of the palm. I would be concerned about risk of fracture and structural failure at that point. The full foliar crown of a mature Canary Island Palm like that can weigh several hundred pounds and represent extreme risk to any underlying property targets or risk for personal injury if it were to break and fall.

No matter what the original cause of infection, wounding, tree climber spikes, chain saw cutting too deep into the pseudobark, I believe that the squirrels are secondary opportunists and not the cause.

Because of the way that palms (monocots) grow, there is no way that I can think of to stop the advance of the decay. Covering the holes will only stop invasive activity but not advance of fungal decay.
This is serious for you safety. You are very near the UCCooperative Extension in Alhambra where Don Hodel is based. He is maybe the top palm expert in the world and has done a lot of research on palm diseases. You may get a free inspection and advise because of UCCE public advisory services.
http://ucanr.edu/sites/HodelPalmsTrees/?facultyid=1022

Your questions are so specific to your locale and conditions, it would be best to contact someone from a local agricultural extension service, or discuss the questions with a certified arborist in your area.

Here's an article on Canary Island palms that may be helpful:
https://www.gardeningknowhow.com/ornamental/trees/canary-palm/canary-island-palm-trees.htm

I hope it is not a palm weevil. Here is more:

https://ucanr.edu/blogs/blogcore/postdetail.cfm?postnum=26668

https://edis.ifas.ufl.edu/publication/st439

https://www.gardeningknowhow.com/ornamental/trees/canary-palm/canary-island-palm-trees.htm

I'm not clear on why there are "cut pieces". You may have weevil damage. Here is more:

https://www.gardeningknowhow.com/ornamental/trees/canary-palm/canary-island-palm-trees.htm
https://edis.ifas.ufl.edu/publication/st439
https://www.gardeningknowhow.com/ornamental/trees/palms-trees/palms-with-pink-rot-fungus.htm
https://www.gardeningknowhow.com/ornamental/trees/palms-trees/ganoderma-in-palms.htm
https://www.gardeningknowhow.com/ornamental/trees/palms-trees/palm-tree-planting-outdoors.htm

This sounds like a drastic negative reaction to environment. These palms do not usually clump, or grow in groups. This stress can be brought about by over and under watering, nutrient deficiency, constricted roots, lack of sunlight, and more.

The larger leafs and lighter color leads me to believe that your original palm will soon begin to die off. The pup can be replanted, however. It color issue can be a sign of lack of light.

I would advise trying to save the original by transplanting. When transplanting a Canary Island Date Palm, avoid cutting its roots indiscriminately as palms are sensitive to root disturbance. Gently separate circling or girdling roots, trim any damaged roots, and inspect the root ball for pot-bound issues. Choose a slightly larger container with drainage holes, water the palm before transplanting, and minimize root disturbance during the process. Monitor the palm for signs of stress and provide proper care to facilitate recovery after transplanting.

This article will give you information on the care that it would receive in nature. This will give you a good idea of what it would need indoors.

https://www.gardeningknowhow.com/ornamental/trees/canary-palm/canary-island-palm-trees.htm