Value flow in economy - redefinition credit and money? There are voices that there are already too much debt in the world (government, personal, government debt) and that can be the cause of the crisis. From the other hand the the only solution offered by the governments and the central banks to the possible (forthcoming or not) crisis is to create more debt. So - if consumers take loans and spend them, then manufacturers can produce and the GDP grows. But if consumers are prudent and save money, then manufacturers can not sell produce and can not continue operations, GDP falls and recession emerges.

If this vignette is true, then how sustainable growth can happen? Or is this vignette the example that there always should be boom/bust cycles? Or does my vignette contain some paradox, some oversimplification, some mistake? My question is - is my vignette correct or does it contain mistakes and what are those mistakes?

One can try to solve the paradox in vignette by saying that consumers create value as well (labor) and that they can spend the money earned with their labor without taking loans and so the sustainable GDP can exist. If that is so, then why governments or other entities are trying to boost credit instead of boosting labor? Some can say that "boosting" labor can be quite cruel - e.g. the governments can put into force laws that pressure citizens to accept any work however bad paid it is (i.e. if there are no betters jobs available in the economy). But from the other side one can argue that government can increase the skill level, the creativity level, the entrepreneurial spirit of the citizens and so they can create new businesses, new ideas, be worthy employees for businesses that pay high wages. So - such boosting of labor can be beneficial for the all (citizens, businesses, budgets; such boosting does not require increase of the debt level). Why such beneficial boosting is not happening? Why central banks does not suggest such boosting and why everything is talking about increase quantitative easing and debts?
Your question is very broad so it is hard to answer but I will try to do it


Can there be sustainable growth without debt? Yes! Most models of economic growth don't even have debt in them. Most economists believe that growth comes form increase in factors of production like capital accumulation and from increases in avaiable technology. Debt can also play role in promoting growth by extending credit to entrepreneurs who are poor, but in most macro models it does not play role in long term growth. 
The vignette that you described holds only in the short run. In the short run it is possible to boost economic activity by 'supporting' loans by lowering interest rate, and in short run savings can exaggerate recession, but this does not hold in the long run (at least not in standard textbook macro models). Regardless, you should not confuse the short run dynamics with long run economic growth. Unless there is some hysteresis effect, which is still controversial, business cycle does not necessary affect the economic growth it just happens around it. Even in presence of hysteresis economic growth would still occur but business cycle could made it permanently lower than it could have been. 
Value does not come from labor - that is an archaic classical economics theory that was since disproved countless times and does not square well with empirical observations. Value is subjective. This being said boosting labor supply definitely increases GDP because going back to the point 1. it increases the avaiable stock of factors of production, although unless you can do it consistently it will lead to level increase in GDP not really to sustainable growth.  
Every single advanced country I can think of has some programs that are trying to improve labor force participation. For example, many countries have earned tax credit, unemployment offices that help people find job, vocational training programs, lifelong learning programs etc. So the "boosting" of labor supply is definitely happening in most countries - in fact the only exception I can think about are some defunct states like Somalia which are in state of anarchy. Of course some states do this better than others, but that's completely different topic. 
It is not a job of central bank to conduct or even suggest labor market policies. Central banks job is to conduct monetary policy and bank/financial supervision in accordance with its mandate. This mandate differs across the world but most central banks have mandate that is similar either to the Fed's or ECB's mandate. The Fed has dual mandate of price stability and full employment, but full employment here means of resources in the economy not just labor and its done through the monetary policy. ECB has only single mandate of price stability so it is not its job to even care about labor supply, except to the extend it can have some influence on price stability. In short central banks talk about quantitative easing and debts because that is their job. It is simply not in their competence to conduct some policies on labor market even if they would want to - that is job of labor department or ministry of finance/economics depending on what country we are talking about.