I burned pcb joints away
Your soldering iron was way, way, way, WAY too hot!

650F for tin-lead solder, 720F for lead free works pretty well for me. DON'T GO HIGHER UNLESS YOU KNOW WHAT YOU'RE DOING!

Ok, fixing this:
It looks like the plated interiors are still there, so you should be able to get solder to wick down if you're careful when you solder a new component in. That will be tricky since it will be hard to get the plated interiors hot... If you can find it, with hot air you can pre-heat the area to about 100C (sorry for mixing units!) before soldering. This will help. Also, use flux liberally to help the solder flow. If you have access to it, leaded solder will probably work better than lead-free too. Make sure to heat both surfaces (the component and pad) if possible. This helps make a good connection. Sometimes you can use molten solder to help conduct the heat into hard-to-reach areas.

On the other hand, if the board is definitely only two layers, just connect the traces on the top and bottom to the component with the following technique:

To restore the connection where the trace is ripped back, use an exacto knife and carefully scrape away the green mask*. This will give you a place to create a solder bridge or drop a small piece of bare wire down to bridge the connection.

*Use eye protection when you do this, because I've broken quite a few of those blade tips, shooting the tiny metal shard straight at my face!