First - your definition of 'demand' is 'completely wrong' and totally at odds with the entire field of economics - even the schools that traditionally disagree with one another.
'Demand' is a function of 'how much people are willing to pay for stuff, and at what price'.
The 'supply' of something is how much suppliers will sell, at what prices.
A change in the supply curve (the cost of something) does not change demand.
It does change much of the item will be sold for, aka the 'market clearing price' - which I think you are confusing with 'demand'.
Please have a closer look the 'Supply and Demand' Wiki entry I referenced.
As for the rest of your thesis:
You're trying to rigidly apply concepts of Supply and Demand in 1) theoretical contexts, which do not exist in reality and 2) you are ignoring the fact that Supply and Demand for goods (like labour) are balanced with other forces, which always alters the equation.
For example, in the case of higher minimum wage:
"They can replace the workers with fewer more experienced ones who will be able to command the higher wage."
It is a 'rigid assumption' that corporations would simply try keep their labour costs consistent.
While it's possible they could do this, 1) there are any number of other things the could do, and2) in reality, they probably won't do that at all, because this idea that an increase in labour cost will materially result in better workers is false.
'Paying 5% more will get workers who work 5% better so we can then reduce employment by 5%' is a fallacious equivocation. There's no real situation in which that equation holds, even theoretically that does not generally hold true.
In reality, any company that 'hires fewer people' (even with a bit of a wage increase) probably will have less output, therefore less revenues - which changes a lot of things.
A company could increase it's prices, while theoretically that might reduce unit sales, it may or may not yield a better situation depending on what the curve looks like.
'Profit' matters, because that's what sets the internal 'demand curve' for labour. In a highly profitable company, the most efficient solution to a wage hike may simply to do nothing, and just pay them more out of profits. That could very well be the 'rational self interest' response which maximizes profits after that wage adjustment.
But all of that is pedantic because nothing in the real world works that way, there are always other variables.
Subway is not selling 'widgets' that buyers have a perfect understanding of, and none of these markets operate efficiently.
They could reduce the size of their meat patties - and customers may be none the wiser and therefore consume just as much (which would result in suppliers getting paid less).
They could raise prices in conjunction with a smart marketing campaign that encouraged people to buy in the same quantities even at higher prices (result is customers paying more).
They could somehow have better morale and more enthused workers who just had better output.
They could do financing restructure and get better terms from the bank (again, supplier paying the price).
They could 'dock the overzealous executive pay programs' for performance failures (executives pay the price).
Finally there are big unknowns/risks and issues with time (aka upgrading tooling to increase efficiency maybe has a long time horizon). I hinted at that with marketing, but the same applies to product, process, market conditions and every other aspect of the business.