Would the worker pay to operate the business? Essentially yes*, the non-wage operating cost of a business could be withheld from the workers' wages to pay for things like the electric bill of the building they work in. This is because the workers of the companies who provide that electricity also have a right to what their labor provides. The other possibility is that the government would pay for these costs through taxes (which is indirectly paid for by the population, of course).
Just because a business is worker-owned doesn't mean that every dollar of revenue is distributed to its workers. All companies would operate more like a union or non-profit company where they are limited in the amount of money they can stockpile, but how that money is raised and spent would be determined by the workers or (more likely) leadership that the workers elect to run the company.
*According to Marx, end-stage communism wouldn't have a need for fiat money and the transition to that state is some form of socialism. Marxists have different ideas for what a government and economy look like in these various stages and how the transition between them happens. Because it's easier to imagine and explain an economy similar to what we currently have, this hypothetical assumes an economy with some form of socialism that uses fiat money, businesses that compete with each other, and the government is some kind of representative democracy.
Great questions. There wouldn't be an investor class or stock market under socialism, as only the workers would have equal ownership of their business, so you are correct to question how the initial capital could be raised. I can think of a few ways. (1) In the case where you are dissatisfied with how your current workplace operates, but the majority of your coworkers vote/prefer the way it is, you could convince enough workers in the minority to split from the existing business and pool part of everyone's savings to create a new business. (2) An individual or group could request a loan from a credit union (essentially a community bank). Remember, banks wouldn't be for-profit, but they can still hold/lend money and collect interest on that lent money. (3) Apply for a government grant or loan. A bank or government may choose not to fund your start-up, in which case, you would have to start and grow from just your savings likely without any coworkers at the beginning. Once/if you grow your small business such that it has some government-decided amount of workers (say 10 or so, as an example), you would be required to divide ownership among all those workers and they may vote for different leadership. I.e. even though you founded the business, you don't have a right to its leadership after it grows to a certain size.
This fundraising wouldn't be too different than how it is today; the only major difference is that you couldn't sell "stake" in your company to an investor or investment company for the promise of rewarding them future earnings.
Ideally, taxes (especially from highly successful businesses) would pay for a universal basic income (UBI) that is above the poverty line, so no one would be truly bankrupt. So in the situation where a business fails to get off the ground leaving the entrepreneur in debt, income from their future jobs or UBI would be garnished to payback the debts.
In the case where an already established business fails, as Evolith mentioned, it's not too different than how it already is; that business's assets could be bought by another company or repossessed by any debtors. The difference is that debtors under socialism can't be investment companies or equity firms, so the repossessed assets would be to recoup the losses of your community's credit union or the government, rather than sold to stuff the pockets of capitalists. That's not to say that there can't be corruption under socialism, look at the Soviet Union; it's just that there is more likely to be oversight and regulation in collectivist, worker-owned communities.