This is the day when many people pull pranks on each other and practice all sorts of deceptions and practical jokes on others in ways that tear each other down. What could possibly be wrong with that? Especially since the these are revealed to be "April Fools" jokes shortly thereafter? Well, let's start with Leviticus 19:11. "You shall not steal, nor deal falsely, nor lie to one another [NKJV]." Pretty straight forward. And in case you're wondering what "dealing falsely" means, the word translated as "falsely" is the Hebrew word "kahas", which deals with deception. The intent of these pranks is to deceive, which makes them contrary to Yahweh's commandments, even though they are quickly revealed to be pranks.
What about when the intent is not to deceive? For example, anyone who checks the date on an article that says outlandish things may quickly notice that the intent is not to deceive, but rather to joke around. (You're not going to find me posting those types of articles or videos, by the way. And I'm certainly not joking around in this one.) Such things follow the letter of the commandment, so they are technically not sinful. But I do not believe that such things follow the heart of the commandment. But I will leave it to you to decide for yourself.
Now, about what happens when someone does fall for your prank or practical joke: As I said earlier, such things tear people down by making them look foolish for falling for what you have said or done. This is the opposite of what we should be doing as members of the Body of the Messiah. For example, 1 Thessalonians 5 is all about encouraging one another. April Fools' jokes do the exact opposite to those who fall for them.
By the way, even when everything else that is done on April 1st is in line with the Bible, that does not necessarily mean that the day itself is okay. The thing that would make it not okay is if it were somehow linked to pagan worship. Deuteronomy 12 makes it very clear that anything that the pagans did to worship their gods is off limits to us! An internet search gives some quite interesting results: While the origins of the day are not known, it would seem that April 1st has many centuries of history of people pranking each other. There are indeed some inconclusive links to pagan worship (links that are probably correct). And there are also speculations of other links. Of course, there are some who interpret the unbiblical practices of a "holiday" as definitive proof of the day's pagan origins. I learned of that line of logic when doing research about Purim and Hanukkah. So make of that what you will. But even without this link, this day goes against every intent of Yahweh's commandments, even when the commandments are not actually broken. It also goes against the intent of Yeshua's teachings of going above and beyond what is required of us.