You can fix corroded traces by soldering a small wire (I use small wires stripped from IDE hard drive cables) in place of where the traces would normally run. You can test if a trace is electrically broken with a multimeter.

That fear really is baseless. The tantalum caps are superior to the aluminum electrolytics in almost every way hence why they are slightly more expensive. Just make sure you have the same capacitance and exact (or slightly greater) voltage replacements.

You can put the boards in the dishwasher if you want; you just have to be careful if you do so because if you don't dry it out well you can accidentally corrode your board. Hence why I just clean with a qtip or toothbrush and rubbing alcohol.