It doesn't necessarily appear to be sick. To me, it almost looks like it's putting out variegated leaves, which some pepper varieties do, like Candy Cane: https://bonnieplants.com/product/candy-cane-pepper/

If you put a plant straight outside without slowly acclimatising it it can suffer. Your plant has sunburn.

Aaarrrgggg. That’s what I was afraid of. I’m actually in San Antonio, Texas and this is the first time I’ve ever tried to grow anything. My parents live a bit south of me and have been very helpful with suggestions. (I come from a long line of Aggies, so I’ve got lots of advice!) I think if we plant them in mid-September, as long as we can get some “good growth,” we should be able to have some cucumbers before the first frost. Not sure if that’s true, though. So I should probably dig this plant up? It’s growing next to two tomato plants that seem to be doing quite well, with no signs of Aphids.

The white areas look like mealy bugs to me. You should realize that Majesty palms are notoriously difficult as "houseplants". They only reason HD sells so many of them is because they grow so fast so can be sold inexpensively. You can spray it with insecticidal soup, readily available. These ARE NOT like most palms in that they DO NOT appreciate drying between waterings, so feel free to ignore the one size fits all for watering palms that suggests that they need to dry out between waterings...., they would even occasionally appreciate sitting in a shallow saucer of water. Higher indoor humidity is good, ventilation, keeping it on the cooler side, and putting it outside for the growing season (depending on where you are). But honestly, coconut palms are easier inside. Good luck! P.S., You might also add a bit of more soil to cover the exposed roots but don't over do it.