That doesn't look too bad at all, just scrub it with vinegar to neutralize the battery electrolyte and then rinse with alcohol or distilled water and dry thoroughly. Those capacitors are just bypass caps on the power rails to the ICs, they are probably 0.1uF (100n), anything you can find that looks similar will have a high enough voltage rating. You probably don't even need to replace it, in most cases equipment will still work with one or two of those missing depending on where they are in the circuit. Even the IC's may well be fine once you clean off the corrosion, I had one that had way more blue corrosion than that on the pins and it still tested fine after I cleaned it.
I highly recommend kynar insulated wire wrap wire for fixing damaged traces. You can form it neatly and use dabs of hot glue to hold it down when you're finished. It's what they used for fixing PCB errors in the factory back in in the days before CAD mostly eliminated them.