1. (even though i'm guessing most of them would like one) In this sentence even though implies that it will not happen. They would like one but they won't get one. 2. (The result can be eye-opening) It means something you didn't expect to see or something that makes you think differently about a subject. Hopefully this helps, if not tell me and I will try to explain it better

Honestly, "even" is a strange word that I have difficulty explaining. But I will try. 1. "Even" is not the important word in this sentence, the important word is "though". You can remove "even" and use "although" or just "though" to mean the same thing, but you can't remove "though". In general, "even" doesn't come by itself when it's followed by a verb. Examples: "We mailed all the letters, even [the old letters]." -- Comes before a noun, this is good. "Anything can help, even [writing] a letter." -- Comes before a verbal noun (the idea of the action), this is also good. "I came to your house, even though [I knew] you were not home." -- Comes before a verb, so we must add "though". "I came to your house, though I knew you were not home." -- Means the same thing "I came to your house, although I knew you were not home." -- Same 2. "eye-opening" means the result is surprising and makes you consider new information that you did not consider before.

Ben Dillon is correct in the comments! For question 1, the sentence "even though i'm guessing most of them would like one", the words "even though" can be replaced with "although". This indicates a situation that happened despite the circumstances. If you say "I did not bring enough enough apples for the class EVEN THOUGH I'm guessing most of the would like one", it means that despite the fact that the optimal situation is that everyone gets an apple, the truth is not everyone will get one. If you say "I understood the sentence without knowing what that word meant, though". It means that you could not understand ALL of the sentence, HOWEVER, you still understood its meaning. The last example is "I am still awake even though it is late at night". It makes sense that if its late at night, I should be sleeping, BUT "even though" indicates that, contrary to the cause (being late), I am still awake. "Even though" can be replaced with "but" or "however" in some cases. In other cases, "even though" indicates that a situation happened that acts opposite to the ideal situation. I hope that made sense!

Question 2: means "revealing" or "informative". "Eye-opening" means it helps you "see" or know more clearly than before