We seem to not know what manna is, yet how do we determine it is kosher? I suppose this is the case because G-d deemed it so, but what do our sources say?
Simply put, it appears that the main rule is that everything is Kosher unless prohibited. So if Mannah does not fall under any prohibition (mainly coming from an unKosher animal) it's deemed Kosher. Not the other way around.
Is bubble-gum or Cola Kosher if it's not on the Torah Kosher list? Yes, if there are no prohibited ingredients in it. Same with Manna - there were no prohibited ingredients in it.
You are right and AlBerko's answer is right. Mana is kosher for each of these three reasons: because it if provided directly by Hashem, because He said to eat it, and because it is not non-kosher.
The Gemara in Chulin (5a) says that the meat provided to Eliyahu by the ravens was kosher because it was specifically brought to him by Hashem's word:
לימא מסייע ליה (מלכים א יז, ו) והעורבים מביאים לו לחם ובשר בבקר ולחם ובשר בערב ואמר רב יהודה אמר רב מבי טבחי דאחאב על פי הדבור שאני
The Gemara suggests: Let us say that the verse written with regard to Elijah supports the opinion of Rav Anan. The verse states: “And the ravens [orevim] brought him bread and meat in the morning, and bread and meat in the evening” (I Kings 17:6); and Rav Yehuda said that Rav said: They would bring the meat from the slaughterhouse of Ahab. Clearly, Elijah would not have eaten the meat if Ahab’s slaughter was not valid. The Gemara responds: Since he ate the meat according to the word of God, the case of Elijah is different, and no proof may be cited from there.
Tosafos there points out that according to the one who wanted to prove that Ahab's meat is kosher, not needing a special allowance, there would still be a problem of unwatched meat, and according to everyone Eliyahu relied on the fact that this was provided specially by G-d that it was kosher.
The general rule is that all foods are kosher until made unkosher. The meat of an animal is in a general category of forbidden food until it is from a kosher animal and properly slaughtered. This is the most basic reason why mana is kosher.
As far as the pasuk "These are the animals", the Gemara (Chulin 63b) explains that this is to tell us that there are more non kosher animals than kosher ones.
Mahn is a "natural" product. It's similar to a fruit or vegetable. It was a product that fell from the sky and was untouched by humans, in the same way that any fruit or vegetable is. It was not any type of animal that needed to be slaughtered.
Except for the possibility of bugs and other insects, I haven't seen a single rav or kashrut org. require any hashgacha for natural unprocessed produce. As for any concern of trumah, ma'aser, etc. you'd really have to go out of your way to show that mahn is produce. Even if it were, they hadn't entered Eretz Yisra'el yet. Even for the short period that they ate mahn until the day after Pesach of being in Gilgal, they still hadn't inherited any land.
We do know that the mahn collected worms, and, perhaps one could ask if it had to be inspected like berries and lettuce does. However, by that time, it was inedible, and all left-overs melted except on Shabbat, and then, it didn't attract bugs anyway.
I think I've made every possible point or concern clear here, and then some...
I see no one posted my comment so I will post as an answer.
The gemara in Sanhedrin 59b writes "Ein davar tameh yored min hashmayim ". A non-kosher item does not descend from heaven.
Context of the gemara (Sefaria translation):
The Gemara asks: Is there such a thing as meat that descends from heaven? The Gemara answers: Yes, it is like this incident: As Rabbi Shimon ben Ḥalafta was walking along the way, he encountered those lions that were roaring at him, intending to eat him. He said: “The young lions roar after their prey, and seek their food from God” (Psalms 104:21), and they deserve to receive food. Two thighs of an animal descended from heaven for him. The lions ate one of these thighs, and they left the other one. He took it and entered the study hall, and inquired about it: Is this thigh a kosher item or a non-kosher item? The Sages said to him: Certainly it is kosher, as a non-kosher item does not descend from heaven.
In connection to that story, it is related that Rabbi Zeira asked Rabbi Abbahu: If the likeness of a donkey had descended for him, what would the halakha have been? Would it have been permitted? Rabbi Abbahu said to him: Foolish bird [yarud nala]. The Sages already said to him that a non-kosher item does not descend from heaven; therefore, it must be kosher."
Conclusion: anything that descends from heaven is kosher and manna is no exception.