3a. Although it's unclear where they get their info from, Dictionary.com makes no claims to it being archaic, and says that "gage" is used "especially in technical use."
http://www.dictionary.com/browse/gauge
3b. Dictionary.com claims the verb "gage" is only archaic when used to mean a "pledge, stake or wager," which is not how it's used. http://www.dictionary.com/browse/gage
4. The Oxford English Dictionary makes no claims to the verb gage used as a synonym for gauge being archaic. Only when used to mean "Offer (a thing or one's life) as a guarantee of good faith" and that's not that spelling, but the meaning which is archaic. https://en.oxforddictionaries.com/definition/us/gage#gage-2
1. I have looked at the Cambridge Dictionary which makes no claims to it being archaic: http://dictionary.cambridge.org/dictionary/english/gage
2. I have looked at the Merriam Webster Dictionary which makes no claims to it being archaic: https://www.merriam-webster.com/dictionary/gage
3a. Although it's unclear where they get their info from, Dictionary.com makes no claims to it being archaic, and says that "gage" is used "especially in technical use." http://www.dictionary.com/browse/gauge
3b. Dictionary.com claims the verb "gage" is only archaic when used to mean a "pledge, stake or wager," which is not how it's used. http://www.dictionary.com/browse/gage
4. The Oxford English Dictionary makes no claims to the verb gage used as a synonym for gauge being archaic. Only when used to mean "Offer (a thing or one's life) as a guarantee of good faith" and that's not that spelling, but the meaning which is archaic. https://en.oxforddictionaries.com/definition/us/gage#gage-2
Concession speech?