Ignition coils are a very common failure on these cars and likely what is wrong with yours. I would suggest replacing all 4 coils and the spark plugs as the most likely fix. Without a little more information which will require some type of scan tool this is my best guess.
Which cylinder got the new coil? Also, have the plugs been replaced recently as part of this problem? I didn't know about the o2 sensor code, was it a p0171?
Ok. You could try swapping coils between cylinder #1 (the new coil) and cylinder #2 (misfire code p0302) and see if the misfire code becomes p0301 (cylinder #1). There is no distributor on your car, the coils are triggered by the engine computer. It is not uncommon to have multiple coils fail near the same time, I would always recommend replacing all 4 coils at the same time, except you have replaced one so just doing the other 3 would be ok. I suspect you have other coil problems since you are getting
p0300 (multiple random misfire - cylinders not identified). But the p0171 could either be a vacuum leak or possibly a bad mass air flow sensor (another common failure on these VW's). Replacing the fuel filter can't hurt and it is not very expensive, I would recommend that anyway. It is difficult to diagnose around worn or old tune up components. Finally, check the grounds for the coils. The brown wires bolted to the valve cover are the grounds, make sure they are clean and tight. Let me know how this turns out for you.