Nios II basic questions

No, not exactly

you have a high level synthesis tool called SOPC that you run from within QuartusII

SOPC generates SOPCStructure.vhdl that you include in your top level and synthesize with QuartusII to get the .sof or .pof to configure your FPGA.

your FPGA can run with the NIOSII beeing inside but Idle, now to make it run the independent process is to:

Start the NIOSII IDE tool, create a project based on the intermediate file .sopcinfo generated by SOPC, write all your C code, compile it to get a .elf file. that is like an exe of NIOSII.

once the FPGA is running with the corresponding .sof file, you can upload the .elf to the memory that the NIOSII will run from.

I'm not going into detail because the purpose is only to give you a general idea, if you keep this solution for sure, then I won't do better than the abundant doc and tutorials around NIOSII.