For #1, yes you can. The steps that I would take would be to first find out what type of ethernet card you have (either by pulling the card out and looking at it, or by looking at the manual if you still have it) and then do a google search for "<insert card name here> driver" and see what you get. More than likely you will find something out there on it. Maybe a zip file or something. Drivers arent all that big so putting on a floppy is no problem. Once you download the driver, goto device manager, find the yellow exclamation mark, right click, update driver, and navigate to where the driver is (floppy if you saved it there). That should update the driver and get rid of the yellow exclamation mark.
As for #2, I am sure there are programs out there that can look at device manager and try to identify what devices the exclamation marks are associated with, but I have no idea of exact names. Do a google search for it and see what you find. Google is your friend
Hope this helps.