You've got a few options here, as I should think that ultimately the solution will be found by the not-sphynx's behaviours and mannerisms (though the questions themselves do help bring those behaviours out).
You could go for something everyone knows, like "What's lighter: a tonne of bricks or a tonne of feathers?" When the players get it right by saying they both weigh a tonne, have the not-sphynx insist on the obvious wrong answer instead (the feathers, as a single feather is lighter than a single brick). Then when the players explain why that's wrong and their answer is right, the not-sphynx pretends he knew that and was just testing them. Stuff like that.
If the campaign isn't super serious in tone, you could work-in famous pop-culture examples. Ask the questions for crossing the bridge from Monty Python "What's your name/quest/favourite colour?" With the not-sphynx not getting that the difficulty came from Tim alternating to a super hard third question for every other person he asked. You can even use the question about the African Swallow, with the not-sphynx not knowing if it should be laden or unladen, and just handwaving that one away when the players ask.
Ask the "What have I got in my pocket" question from the Hobbit. The players might try and answer "The One Ring" or something clever. When they exhaust their ideas and give up, the not-sphynx gets embarrassed and plays it down, admitting he forgot he doesn't have any pockets...
Cool idea overall though - I think your group will have a lot of fun.
I don't play anymore, but did for about 10 years.
I started with 1-1 lesson, but I think I only kept that up for a year or so.
I think the biggest things you'll benefit from through 1-1 lessons are:
1 - getting some solid musical theory behind you (a bit of a bore, but useful when you're trying to self-teach later on, and ultimately foundational to pretty much everything else).
2 - Having someone there who can see, hear, and correct your actual playing technique. Poor technique absolutely ruins you as a musician when it comes to progression and trying to play anything a bit more advanced, because it becomes part of your muscle memory. That's why it's so important to slow things right down and play them correctly, with the right technique, and then gradually speed up, rather than jump into playing things at the correct speed, but doing it sloppily. Having an instructor who can observe and correct you in real time will do wonders.