How can I repair these rusty electrical connections?
I would strongly encourage you to replace this unit (the Siemens component, not the entire AC) and replace the ends to those electrical wires. Simply put if the rust situation is that terrible I wouldn't be at all surprised if the integrity of the unit is already compromised, i.e. ready to fail you at any time. Your yellow wire is almost certainly why it's not working now, but it's a pain to fix it, and then have to fix it again only a few days/weeks later.

This is not a normal amount of rust; a great deal of humidity is getting to it, more than usual. I'm a Florida resident who had a 12 year old AC unit at one point that had been through a number of hurricanes and tropical storms, and it was only slightly oxidized, no rust. (Though I had to regularly open it for service because for whatever reason ants loved to commit suicide by throwing their bodies in between the electrical contacts)

To fix the rust you'll need to find where it's getting exposed to so much humidity from. Likely a seal or gasket is bad. You can either replace the broken seal/gasket or there are after-market products used as essentially spray on sealants. I recommend fixing it properly and replacing whatever seal or gasket is broken, but in a pinch squirting some sealant into the location that's leaking (with the AC OFF and given enough time to dry) will resolve minor leaks (depending on the severity).