Under a price fixing system you didn't have to deal with inflation you don't want because you (the government) set the price, thus by definition you didn't have inflation (outside of the black market anyway) if you don't increase prices. Instead, the problem you had to deal with were shortages (as the Soviet Union actually have to deal with) because prices don't adjust. Note that this wasn't always the case and there were bouts of inflation in the Soviet period, but unlike in a market economy, you could always just fix prices to avoid it and exchange the problem of inflation for the problem of people waiting in long lines to buy consumer goods.

The banking system was completely state ran, capital allocation was done through the bureaucracy. Household savings etc would be handled by the Sperbank, Investment was handled by the Stroibank, and another bank ran foreign exchanges. Above those you had the Gosbank, which was the core of the state banking system. In effect, the USSR had a single state ran banking monopoly.

Money sort of mattered when you are dealing with the consumer economy, workers were paid in wage, and bought goods in wage. However, cash didn't factor into the equation when you start talking about exchange between enterprises. If enterprise A transfers raw material to factory B for use, the Gosbank would oversee the process and credit A's account while debiting B's account without direct exchange of money between those two entities.

One implication of this is, of course, that inter-enterprise lending is not allowed because there is no mechanism for it except through barter (which did take place). Enterprises in the Soviet Union were forbidden from holding onto cash except paying worker's wage.

Foreign trade was conducted through the Vneshtorgbank. An enterprise producing trade goods would first sell it to the Vneshtorgbank, which would then credit its account, then sell it to foreign countries for hard currency. Which it would then hold on to until it needs it to buy foreign imports, which it would do with the foreign currency it holds. Then it will sell the imports to a Soviet firm, debiting and crediting accounts as needed in the process.