Unless I've forgotten about it, there isn't a way to automate the sync tool at the moment; you can only use it through the GUI and the Set command can only toggle whether the GUI is displayed or not.
I would probably use external tools (e.g. WinMerge) for both jobs, although I think you can use the Select command and a saved filter to do the second case, so that if you select a file in the left side and click the button the same file will be selected in teh right side if it's name and, optionally size and/or date (and/or contents, I think) are the same. See this thread for some details.
Myself, I've made a button which runs the Windows binary file-compare tool (fc /b) on the two selected files, so I get a window open up which tells me the result, rather than having to check to see what was selected after the button was clicked:
<?xml version="1.0"?>
<button display="both" effect="gray" label_pos="right" separate="yes">
<guid>{0BA52189-7F38-4CB8-A21F-C8DB9BB9E526}</guid>
<label>Bin F</label>
<tip>Binary Compare -- Files -- Source vs Destination</tip>
<icon1>AE-Icons\AEi-Diff-20.png,0</icon1>
<function type="batch">
<instruction>fc /b {filepath$} {filepathdest$}</instruction>
<instruction>pause</instruction>
<instruction>@nodeselect</instruction>
</function>
</button>