You have a fantastic collection @stephneechan, great work.
I can’t give you a complete answer, but from what I’ve found they appear to be known as zukan (図鑑) cards, but that’s very vague as “zukan” translates as: “an illustrated reference book, such as a field guide, bestiary, guide book, or picture book”. It’s the latter part of that translation that these cards seem to be known as: they’re “picture book cards”, but they appear to be much more commonly known as “zukan cards” in English. Here is a Google image result for “zukan cards”, and it’s possible to find them on eBay using that as a search term (there aren’t many of the listed at the moment).
What ‘picture book’ are they from? No idea.
Who made them? Bandai.
When are the cards from? ~2004-5.
How many cards are there? At least 400, maybe upward of 600.
I have 2 Pichu cards from this collection, and interestingly one of them is marked “P” instead of having a number and has a lenticular effect. I’m missing at least 1 other card (#133), but it looks like there are only 2 of each card in the set, so I have the feeling both Magikarps are listed here - the reason there are more Pichus is because one of them is a Pichu Bros. card.
As was stated above, it’s the Fan Club Magikarp, easy way to spot it is that it’s missing the 3-star rarity symbol at the bottom right, and that it has a different holo pattern than the actual Shining Magikarp ^^