Caveat
Your main question is simply too broad to cover in SE format so this answer will focus only on the 3 further sub-questions.
tl;dr
The premise of the question is actually not generally valid. Economic growth is not driven primarily by population growth, especially not per capita economic growth (which is what matters for living standards). However, suppose that there will not be any economic growth for some other reason. The short answers to your 3 questions would be:
A1: This would put stress on the pension system. However, It would not make the pension system unworkable as pensions can work on the same principle as an insurance and that does not require economic growth for it to be viable. Nonetheless, at the same time it would make pension schemes more expensive which would mean people would have to either; a) work longer; b) have lower pensions; c) payments into these pension plans (or taxes in case of government) would have to increase.
A2: I can't see any economic reason why this would affect fractional reserve monetary systems in any way whatsoever. In fact this won't be further addressed in full answer because there is not much more to say about it. Fractional reserve system simply works equally in a falling, stagnant or growing economy.
A3: This would not have any effect on inflation in itself ceteris paribus, but there could be some effects caused by the way the government chooses to respond to the issue of no growth.
Full Answer
Addressing the Premise
Before addressing the questions let me address problems with your premise. You argue that:
If the growth rate for the population is low, it would take considerable effort to maintain existing growth rates in the economy, since the number of people available to produce capital would be growing at a lower rate or not growing at all.
This is simply not a generally accepted view in growth literature.
First, what matters for the economy is growth per capita (per person) not just economic growth in general. For example, if GDP doubles from 100 to 200 but also the number of people increases from 1 to 2, GDP itself grows but per capita GDP in both scenarios is just 100. It is growth per capita that matters for material welfare of people (see discussion of living standards in Mankiw Macroeconomics or Blanchard et al. Macroeconomics: a European Perspective).
Second, most economists don't believe that per capita growth has much to do with population growth. In economics there are two main strands of literature when it comes to economic growth. There are exogenous theories of economic growth and endogenous theories of economic growth. Both of the above mentioned strands of literature agree that per capita economic growth is caused by increase in technology but they disagree on what can cause increase in technology. In the exogenous growth literature (which is actually more dominant) population growth has no effect on GDP per capita whatsoever. In the literature on endogenous growth it might have an effect on GDP per capita through R&D (more people means more scientists) but even most endogenous growth models what matters more than population is investment in R&D and share of population devoted to producing R&D. Even in the small subset of models zero population growth would not lead to zero growth per capita - only to lower growth than otherwise (see discussion in Ch 1 and 3 in Romer Advanced Macroeconomics and Barro & Sala-i-Martin Economic Growth). This being said for the rest of the answer we can just assume zero economic growth as a thought experiment.
Answer to question 1 on pension systems
Zero economic growth and population growth would definitely put a stress on pension systems but they do not require economic growth or population growth to operate.
Generally speaking pension schemes work on a similar principle as insurance. In fact you can consider it an insurance for reaching a certain age. Such a scheme does not require growth in population or economic growth per se. However, economic and population growth make these schemes cheaper for the government (respectively people in case of private pension schemes).
Population growth makes pension schemes cheaper because it improves the dependency ratio (i.e. how many working age people support one retiree - see further explanation at Eurostat). However, dependency ratio is affected by large number of things that are completely in control of government (company offering pension). For example, retirement age directly affects dependency ratio because people at some point die from old age. Thus, in principle if you set retirement age high enough you can get as favorable dependency ratio as you want.
Next the economic growth helps in the case of government pay as you go schemes because it increases peoples income and thus indirectly taxes that government collects (20% tax from €1000 is higher than 20% tax from €100). Hence as government budget grows over time these pensions can become more generous. In absence of any economic growth government would just have to face tighter constraint on its spending. In the case of private insurance where retirement money are invested an additional problem would be that if there is no growth investment opportunities will be low to none. However, this just means that money people save for retirement do not accrue interest. But pensions can still exist they will just not be such a good deal for people anymore as before.
If there would be no population and economic growth governments (people) could in principle adjust to the situation by:
- Increasing the retirement age. This automatically improves the dependency ratio as if there is less people who are eligible
- Stop increasing pensions over time.
- Increase taxes (payments with private schemes) to raise more resources for such schemes.
- Make pensions less generous.
The above might be serious political issue but from economic perspective it is completely feasible. Political problems are for political scientists to worry about.
Answer to question 3 about effect on inflation
There does not need to be any necessarily. Inflation is determined by changes in price level which in turn depends on what the money market equilibrium is. This is given by equation of exchange (See Mankiw Macroeconomics pp 87) as:
$$MV=PY \implies
\ln P=\ln M+ \ln V− \ln Y $$
Where M is the money supply, V velocity of money, P price level and Y output. In the log-linearized version the effects of right hand side variables can be interpreted as % changes. If there is zero economic growth that means $\Delta Y = 0$, which holding everything else constant would have no effect on price level.
When it comes to the other variables $M$ is under control of the government. Hence, it can stay put in principle. One could argue that due to lack of growth government might face higher pressures on monetary financing (due to the problems discussed in previous answer for example). But this would not be caused by the lack of growth itself.
Lastly, $V$ is historically very stable, although it does depend on interest rate. To be more specific generally when interest rate decreases velocity also decreases. To the extend that zero growth would cause drop in interest rate it would lead to deflation equal to the rate at which velocity dropped. However, velocity cannot drop forever (if velocity is 0 that means money are not used in economy at all). So there would be temporary deflation, which could be offset by government increasing money supply proportionally as to keep prices constant.
