The normal market solution to a shortage is to raise prices until there is no longer an excess of supply at that higher price
In economics, outcomes are all that matter.
The only thing preventing restaurants from changing their prices is the 'penguin on an iceberg' issue. You may be correct in raising your prices, but if other restaurants are willing to lose money longer before they raise their prices your business may suffer/fail because of it before the rest of the market changes their prices/wages.
So as a restaurant, very roughly speaking, you basically can raise prices until the line starts to go away. Unfortunately customers can be very stubborn and would rather wait in a 1hr line somewhere else, or not go out at all, for quite a while before eventually coming around to the new normal and accepting your new, higher price.
And you will still probably end up with fewer restaurants along the way, as those least-profitable and with the shortest lines outside, go away.
Restaurant sales are rarely made up of price conscious buyers. Sure there's a limit, but short of the blue light special crowd, most customers are eating out for either variety, social reasons, or being tired of cooking.
Yes. This is exactly the question answered by the concept of supply and demand curves. Of course you can argue about the shape of those curves but their existence is not in doubt.
Yes. A so-called “observed shortage” is not a shortage, its just buyers wanting a good without wanting to pay the price it costs to buy in the present market conditions.
A real shortage involves either a constraint which prevents price adjustment to an equilibrium of supply/demand or demand and supply curves shaped in such a way that no equilibrium point exists (which, I guess, is just a very special equilibrium-preventing constraint.)
The solution to an observed shortage of labor is “employers pay more and quit whining”.
The solution (if it is solvable at all) to a real shortage depends on what constraint prevents equilibrium from being reached.
But there can also be a fuzzy area here. There may be situations where most sellers have not raised their prices to respond to decreased supply (for a variety of reasons), and therefore other mechanisms (like who gets in line the earliest) determine who gets to buy. At the same time there may be a small number of sellers who do raise prices (think of the toilet paper hoarders who resell on Craigslist at huge markups). If you consider that higher reseller price to be the "market price" then that wouldn't wouldn't strictly be a shortage, but if you consider the unchanged price to be the market price then that would indeed be a shortage. (In fact, this is why for every natural disaster there are articles with headlines like "Price gouging is actually a good thing; it's the solution to shortages.")
No, that would only be true if there was not an observed shortage; that is, if the current market price was clearing the market with no unmet demand at the market clearing price.
An observed shortage that is not a real shortage means that the market price can rise to the point of market equilibrium without reducing quantity traded. In fact with a normal supply curve shape, the minimum price increase to achieve equilibrium will increase the quantity traded compared to the status quo, as quantity supplied will increase with price. Quantity demanded will be lower than in the status quo, but since the “observed shortage” is quantity demanded being above quantity supplied and, therefore, traded at the current price, that reduction is literally just reducing the “observed shortage” to zero, not reducing quantity traded.