Sorry I can't answer all of your questions, but anyway...
2: I've never heard of ECCp having any problems with any program (and from personal experience I've tried it along with everything you mention except Opera).
3a: To make it disappear (with the statsaholic client anyway, not sure if this works with the default one), you can change the line that says "NO_TRAY_ICON=0" to equal "1" instead of "0", and that will make it's tray icon be gone. If all of the computers can access the 'net directly, make sure that "PERM_CONN=0" is changed to equal "1" also. However, if you're on dialup, you're going to need to call up the ECCp client occasionally to send in the results. To do this, make a file called something like "showeccp.bat" in the same folder that ECCp is installed in (if you do this in notepad, be sure to enclose the filename with quotation marks - otherwise, you'll end up with a showeccp.bat.txt file, which isn't good). In this file, put in this line:
echo . > eccp_show
What this does is to create a small file called "eccp_show". The ECCp client frequently checks for the existance of this file, and upon seeing it, will proceed to delete it and then show its window, until you click "hide" again. Thus, to bring up the client, you may simply enter the ECCp folder and click on said batch file.
3b: You could put a shortcut in the startup folder (make sure that it's set to run minimzed in the shortcut properties), but that might not be discreet enough. In this case, I think (but am not sure) that the Windows Registry can help you out. In Regedit, nagivate to HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Run\ - now, once you're there, choose to make a new string value (in the Edit menu on my WinXP Pro machine here), and enter a name for it (which doesn't really matter, so put anything you like in there). Your version of regedit may also ask for the data at this time; if so, enter the complete path to the ECCp executable, like this:
D:\Program Files\eccp109\eccp109w.exe
If your regedit doesn't ask for the data automatically, and just makes a blank string value, right click on said value and choose to Modify it. Then enter the complete path and filename as specified above.
Edit for grammar and spelling [or, more accurately, lack thereof] 😉