To me, the meaning is same. The only difference may be that "humid" sounds lightly more formal.

It works very well, I've used it for 4 months :)

"I also hope so" and "I hope so too" are both correct, and acceptable in written or spoken language. The meaning is the same for both. To me, "I hope so as well" does not really sound natural.

Your second interpretation is more correct. Bill Gates is referring to a distinct period of history, the time in which he and the audience were living. In saying "the promise of this age", he is referring to the inspiring possibilities of that time period.

Yes, you're correct. In a job description, "single face" would mean that one candidate has several roles or responsibilities when providing service to customers or clients. To refer to a company as providing a "single face" is arguably not the best use of the phrase, but it is not technically incorrect.

You are correct in saying that "take on" means to undertake (or to assume responsibility for). However, in this context, Bill Gates does not require the students to do anything. He is simply encouraging each student to choose an issue or problem that resonates with them, and dedicate themselves to solving it. The choice of which issue to "take on" is up to the student. The line is meant as an inspirational call to action, not a command or demand.

This is close, but with a few corrections: 1. "Extincted" is never used. "Extinct" is used for all tenses, e.g. "The dinosaurs went extinct." 2. "Neither" is only used when referring to two items in the negative. In this case you would use "not". 3. Depending on the context, "heritages" should possibly be the singular "heritage". So your corrected sentence could read: Should traditional living styles go extinct, cultural heritage would not be carried forward.