"It sounds like you are being given the opportunity to build someone else's Minimun Viable Product for free!"
I second this. I have no way of evaluating the character of your boss, but there are warning signs all over the place.
My story: I was hired to build a MVP (did -eventually- get paid) and due to various missteps, it turned into a one man job (I was the entire IT staff for 4 years). Part of those missteps were me being work-obsessed (a bad trap to fall into, it leads to burnout) and the other misstep was that these founders, who had no experience in IT, were all psychopaths (as in one had a criminal history of fraud, the other should have been jailed long ago). I failed to do one of the basic tasks of business, which is know who you are dealing with.
They used my "enthusiasm" which in the IT/startup world is quite necessary, and leveraged it against me. I certainly knew enough at that point in my career, but it got lost in the need to keep things working. Eventually I wised up, when a customer made legal threats because they had been blatantly lied to about the product they were buying.
I, as <u>nominal CTO</u>, had not been paying attention to the sales process and stupidly was relying on the others to take care of that area. It was then I realized the full nature of the whole operation and how I'd been taken advantage of - so I quit. I reasoned they were going to fuck me over one way or another down the line, so I'd better get out.
Less than a year later, the CEO abandoned his wife and kids <as in literally disappearing one day> (she owned 51% of the company) and now they are still fighting it out in divorce court. The CEO turned out to have a 25 year history of fraud and cheating even the companies he worked for.
So ... the people you are dealing with --may be-- great, but you have no real world experience in how businesses are run or how life actually is at the C layer. Read up on the Sociopaths/Clueless/Losers theory - it is a valuable thing to know, as it explains a lot. I've seen shades of it over my 30 year career in IT, but it never hit home till I did this startup.
And if you are really CTO, and a salary of $0 is being offered, why have you not mentioned the percentage of equity offered? If you really are going to be responsible for hiring and designing the tech side of the company and ... you should be getting a large chunk of the company. It is irrelevant the company already exists - by being an official CTO, you are taking on a lot of responsibility.
No offense intended, I'm sure you're capable of programming and all that, but ... I wouldn't hire a 24 year old with just a few years experience as CTO. The Master's is irrelevant in this situation - there is a lot of non-IT social type knowledge needed, IMO. The politics of business is nasty stuff, and your stereotypical engineer (i.e. me) likes to stay out of that stuff; it is a skill set you have to either like (and so you're an asshole) or you just get used to it. I've always tried to stay out of it, hence the 15 year career of contracting.
I think my advice is, if you want to stay with this company, then say you want to be "Lead Architect" and leave the management/business stuff to someone else - then you can expect to get a salary and will only be tangentially exposed to the business/political crap that typically goes on - that way, you get some valuable non-IT experience safely and some tech experience too. When (not if, this all doesn't sound like a winner) the company crash and burns, you'll have some useful profit out of it.