Remove the two diodes now, and check them separately - one will probably read OK, and the other read as faulty (as they did in circuit) - as I said earlier they BOTH need replacing, with rectifiers from the same batch (out of the same bag).
For repairing the tracks, I usually use the inner solid core of satellite TV coax (CT100), or for a bit thicker the earth wire from 2.5mm T&E cable, or even the live/neutral cores from 2.5mm T&E. You simply solder it along where the existing track goes, scraping off the resist along the track so you can solder to it, and running the wires from component joint to component joint.
On the first picture, immediately to the right of the rectifiers and burnup, there's a large electrolytic, and between the two horizontal connections there's a small hole in the PCB - you should start the wires from those two connections, and run them along the relevant tracks over the burnt area. If the track is too badly burnt, then cut the track away in that area - and if the board is excessively charred, then scrape the burnt area away, even if that involves going right through the board (the solid wires you're fitting will support themselves across the gap).