Would this history not matter anymore?
It would matter a lot. It's why this situation is unfortunately fictional. A revolution needs a historical process to drive it and US history is dominated by the process of settler-colonialism. A revolutionary moment will be quickly hijacked by (insert any caricature of US politcal stereotypes) and will serve the development of settler-colonialism.
Would USSA schools still educate children about her? What will happen to the philosophers that influenced U.S culture?
Im deeply uncomfortable with a "USSA" but beyond that the answer is an easy yes. History will be taught.
What would happen to Mount. Rushmore? Would they be replaced with Soviet and communist figures instead?
You mean The Six Grandfathers?
US monuments will fall and Indigenous sacred sites will no longer be desiccated. Why Soviet leaders should be depicted in monuments is beyond me. We have our own history and our own project to construct.
What would happen to their trillions of debt? What ties would you cut, and who would you ally the USSA with next? China? What countries would you have relations with? Who would you do trade with?
Debt forgiveness is one of the most important features of any transfer of power and would effectively nuke rent seekers from orbit, destroying their power.
The former US would need to reshape its economy. If the global economy was made equitable today the standard of living in the US would collapse in a way that makes the great depression look like a theme park ride. This isnt even considering there will be conversations about reperations. I doubt this could be fixed by trade. Socialist construction would have to reshape everything and frankly it could take decades to recover from the end of imperialism. We would likley need expertise from those who have tread this path, meaning China would be an important partner. Perhaps a balanced relationship could be established with the world by giving technology held behind IP rights.
What businesses would you shut down immediately?
I dont think we'd have to worry about much of this because many businesses could evaporate. Fast food being one of them. I personally might target specific commodities that have colonial history and seek to restructure them equitably and destroy our entitlement to these communities. Sugar, coffee, tobacco, tea, etc.
What are your efforts to make the USSA a strong country and incapable of being attacked by capitalist imperialists?
Honestly if the US collapses capital loses its sword and shield. The world could trend toward socialism without much imperialist intervention. It would be a totally new era that is hard to imagine.