size difference between reg and X large?

I can't tell you that. But the digits on the display screen are 1 full inch tall and 1/4 inch wide. The numerals are a dark black and have a better contrast against the grey background than most LCD displays. The keys on the calculator are 7/8 of an inch wide by 5/8 of an inch tall. The numerals on the keys are a bright white that are between 3/8 and 1/2 an inch high. The plus and equal keys are 3/4 inch wide and a full inch tall. I really like the calculator. It is great for an older person with vision difficulties. I have glaucoma and my vision is diminished. The calculator probably would not be sufficient for someone who is legally visually impaired with 20/200 vision or less. I think it should work for someone with macular degeneration because the numerals are large enough to be seen using one's peripheral vison. I hope this helps.

Do the keys have "tactile feedback," ie can you feel a "click" when key is pressed or are they "mushy?"

Yes, you can definitely hear a slight click every time a key is pressed. They are definitely not mushy as they are plastic.

How is the battery replaced? (no images showing battery door)

It is a rechargeable battery and charged via solar cell. Probably not much of a battery at all because it does not need one. Any place that has light will have enough light to run this calculator. Mine has 2 phillips screws near the top on the rear of the unit but I have not taken it apart and will never have a reason to because if there is not enough light to run it then, I will not be able to read the digits anyway. (The display is a nice, large LCD)

Without an “off” button won’t the battery be in constant use?

No. The calculator shuts off after about 7 minutes of not being used. I just tested the shut off. (The calculator operates on both battery and solar power.)

Display Size	4.5 Inches
Color Name	ピンク
Batteries Included	Yes
Batteries Required	Yes
Brand	CATIGA
Manufacturer	Jeoly / Catiga Electronic Co. Ltd
Item Model Number	CD-2786-12
Display Type	液晶
Product Dimensions	15.24 x 11.99 x 0.25 cm; 200 g

デスクトップ電卓 12桁 大型LCDディスプレイと敏感なボタン付き ソーラーとバッテリーデュアル電源 標準機能 オフィス 家庭 学校 CD-2786 (ピンク)

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デスクトップ電卓 12桁大型LCDディスプレイと敏感なボタン付きソーラーとバッテリーデュアル電源標準機能オフィス家庭学校 CD-2786 (ピンク)