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Your problem is powdery mildew, which is a fungus. Here is an article or two that you may find helpful: https://www.gardeningknowhow.com/ornamental/flowers/hibiscus/answers-to-what-causes-hibiscus-leaves-turning-yellow.htm
https://www.gardeningknowhow.com/plant-problems/disease/powdery-mildew-homemade-and-organic-remedies.htm

Yes, these are the fruits of the tree and you may cut them if you like.

Areca Palm do need repotting every few years, to refresh the soil.
They do prefer to be in a more confined pot, too large of a pot can lead to over watering and root rot.
They do not like their roots to be disturbed to the fact that you unpotted the plant twice has let to some shock.
You need to make sure you replanted the Palm at the same depth that it was growing previously.
I think that may be the reason you are seeing some strange 'white, new fronds growing' from the base.
You can correct the planting depth and make sure you are watering correctly.
The yellowing fronds can be due to too much sunlight, too much or too little water.
Here is a link to refresh you on the care requirements.

https://www.gardeningknowhow.com/houseplants/areca-palm/growing-areca-palm-indoors.htm

There are very specific reasons for repotting an Areca Palm, and this article will give you the reasons why as well as the "how." Hint: you'll want to remove your new Areca Palm from the original pot -- it is not needed any longer.

https://www.gardeningknowhow.com/houseplants/areca-palm/growing-areca-palm-indoors.htm

This article will refresh you on the care requirements.
https://www.gardeningknowhow.com/houseplants/areca-palm/growing-areca-palm-indoors.htm

It is quite possible that you should fertilize with a half strength fertilizer, although some coloration is normal. This could indicate a nitrogen deficiency. Here is an article for more information on the care of this palm:https://www.gardeningknowhow.com/ornamental/trees/bottle-palm/caring-for-bottle-palm-trees.htm