Not actually sure I can see the damage. Did that just break off completely?
If it did, you need to inspect the pads to see if they are still on the PCB, you can quickly try tinning them (whetting with solder/flux) Which you will need to do in prep for the connector. If not, you will need to scratch down to expose the traces nearby and splice in some bare wire to make contact with each pin on the connector. After that, hot glue to give it some strain relief and cover the exposed wire/traces.
As for the soldering itself, don't worry too much about bridges, if they happen heat it up again and try and let the natural flow separate the two pins. If too much solder is there, use some desoldering braid to wick up some of the solder (you could also use one of those little vacuum/suction tools)