The Shulchan Aruch (OC 131:6) brings down the minhag not to say tachanun on Tu Beshvat. It is quoted earlier in the Beit Yosef in the name of the Rokeach (Siman 312 in the Rokeach according to the Beit Yosef but I don't see it there). The Beit Yosef (quoting the missing Rokeach) says the reason is because it is the Rosh Hashana for trees. The Gra on the ...
I may have found them myself! To clarify, this is not the Yehuda HaLevi of the Kuzari; it is the other Yehuda HaLevi, a student of Eliezer HaKalir. They are brought in Sefer Tehilla L'David, a collection of Torah sources on Tu B'Shvat. Here it is: hebrewbooks.org/pdfpager.aspx?req=20613&st=&pgnum=254
The question was asked by the Satmer Rav quoted here. As cited there he answered
The customs are indeed appropriate. On the day when trees are “judged,” we are interested in determining the success of the tree during the previous year. That is done by assessing what it has produced. On the other hand, when our focus is on the fruit and we want to assess ...
See on the Seforim blog:
There are those who claim the custom to celebrate Tu-beshevat as a holiday is based upon the book Hemdat Yamim. This book, according to many, was either written by Nathan of Gaza (Shabbati Zvi's "prophet") or one of follower of Shabbati Zvi. (This is contrary to the assertion in the Philogos that Nathan is not author, a contention ...
Sefer Chemdas Yomim from Rabbi Binyomin HaLevi in Tzefas brings down the Seder in the following links
According to here:
It is said in the name of Rabbi Chaim Vital that one should endeavor to eat thirty different types of fruit on Tu Bishvat: ten different fruits which are eaten in their entirety, ten fruits of which only the interior of the fruit is eaten, and ten fruits in which only the exterior is eaten. Other kabbalists teach that only 15 different ...
Thanks for the link to the Hebrew text - it just came in very handy! Let me add that Galaski's translation is indeed in the JPS-published anthology Trees, Earth, and Torah, edited by Ari Elon; I own a paper copy but have also been able to access the whole of that section on Google Books.
I think there are a few factors that significantly mitigate the magnitude of the problem:
As indicated in comments by DoubleAA, most of Israel's major fruit crops' harvest seasons are not in Shevat-time. See, for example, this contemporary calendar, which lists months between June and October for figs, pomegranates, olives, and dates. (It says "year-round" ...
As noted by various commenters, this is clearly due to the order of the calendar. My only addition to this answer is that similarly (although likely due to error), in almost all old editions of Mishnah Berurah, laws of the 4 Parshiyos (which take place in Adar) are included in Hilchos Chanukah. See here (next page too), for example.
Well there's this Rabbi Adir HaKohen who brings a small siman (from Rosh HaShanah daf 14b) for why the focus is the evening.
In addition, here's a collection of halachos for Tu BiShvat, where the rabbi brings one source for day (Even Yisrael) and two for night (Yafe LaLev and Moed Lekol Chai). Do not know these sources well enough, sorry :)
On Shavous we are indeed celebrating the fruit of the tree. One of the opinions given by the Midrash of the Etz Hada'as was that it was Chitoh. The Shtei Halechem, the only korban made from wheat, was brought on Shavous, (the Ritvoh connects the two ideas) the day that the tree is judged. The judgement of the tree is strongly tied to the judgement of the ...
Sefer Nitei Gavriel says that on Shabbos we have fruits at each of the three seudahs; he notes that it should be after the regular courses are served in order not to diminish one's appetite for the Shabbos seudah.
Tu b'shvat is one of the four Roshei Hashanah brought in the first mishna of maseches Rosh Hashanah. These days generally have a status of Yom tov, or at least a semi-moed, and therevore are days of some type of simcha, and we do not say tachanun.