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Removing the flowers from the plants will not harm them, so go ahead.

This is most likely a deficiency in potassium and magnesium. Apply a fertilizer that is listed as 8-2-12-4.
Measure and follow the directions for the chosen product. Apply every 3 months during it's growing season.

https://www.gardeningknowhow.com/houseplants/pygmy-palm/grow-pygmy-palm-trees.htm

Yes, they can do very well in containers. They have a smaller root ball so they can stay in the same container for years.

https://www.gardeningknowhow.com/houseplants/pygmy-palm/grow-pygmy-palm-trees.htm

If your temperatures drop below freezing you will need to move this plant indoors for winter.

Here is a link that will help you.
https://www.gardeningknowhow.com/houseplants/pygmy-palm/grow-pygmy-palm-trees.htm

It can be easy to overwater or overwhelm the roots if you choose to large of a pot for the plant.
Make sure the soil is well draining and that the soil is moist but not soggy. The top couple of inches of soil should be dry before watering again.
Check the soil, don't water on a schedule.
A Pygmy Palm will actually do fine with brief periods of drought.
Protect the palm from drafts from heaters or air conditioning.
Bright indirect light location is best for your palm.
You can mist your plant regularly to keep it clean and pest free.

https://www.gardeningknowhow.com/houseplants/pygmy-palm/grow-pygmy-palm-trees.htm

Check for any other signs of pests or disease.
A Pygmy Palm needs regular watering in sandy, well draining soil.
The article below will refresh you on the care requirements and some particular nutrition needs of the palm.

https://www.gardeningknowhow.com/houseplants/pygmy-palm/grow-pygmy-palm-trees.htm