> It could turn out that some of the existing wiring has conduits that could be used
Unless it is low voltage in the conduit, you don't want to mix 120v with low voltage wiring.
In residential, it's not a huge deal but does come with the risk of data loss along with, to my understanding, an extremely minimal chance of fire due to inducing voltage. The chance of fire increases as the voltage goes up so generally it's only a risk in commercial or industrial.
You don't have to get inspections or follow code to my understanding but the rule of thumb iirc is 8 inches minimum between low-voltage and 120v. So if 120v is in one stud 'bay', you go to the next one.