Not sure that the rolls is a particularly well regarded brand. Suggest that if you need to use a phantom power adapter, you acquire a battery operated one. Denecke make one that takes a 9v battery and provides phantom across two inputs. Phantom is very low current so a 9v battery would last a while. This will avoid any issues with a power-supply.
a. Make the setup work with the new balanced audio cables and restore the fidelity of the audio.
You don’t have new balanced audio; you have unbalanced stereo going into a balanced input which does not work and is why the audio sounds horrible and like things are missing. (Because they are.)
b. Change the setup in a way that the 1/8" to 2x 1/4" ...
I replaced the unbalanced cables with 1/8" to 1/4" cables, thinking that would fix it.
That's still an unbalanced cable. Your PC output is unbalanced, any cable connected to it will be unbalanced.
You could insert a DI between the PC output and the mixer. Use a passive DI or an active DI with a power supply. Experiment with the Ground lift switch.
Firstly, do any and all processing in WAV files. If your source material is on CD, then rip to 44.1kHz/16bit WAV and process at 24-bit in your software. Do not transcode via mp3.
Tracks like 104b should be discarded. There is nothing you can do with files like this. The studio has not done their job properly. They have recorded the transfer with input ...