We will be traveling to Europe in July. Paris (4 days), Lucerne (2 days), Gimmelwald (2 days), Fussen (2 d), Rothenburg (1 d), Bacharach (2 d), Haarlem (2 d), Brugge (1 day), London (4 day). We are thinking of buying 4 country Eurail Pass. How many train days do we need? Would we be able to save some money by purchasing Swiss Pass or Bahn Card?
A Bahn Card with Deutsche Bahn is a yearly subscription, I don't think this is what you want. Waiting for Lee to explain to further explain advanced purchase and regional rail tickets...
I don't try to analyze travel outside of Germany, but for there, you don't need a railpass. If you book before others get the best fares, you might get Lauterbrunnen (not Gimelwald) to Füssen for as low as €39 (the best I could find for mid-July was €109, so you might already be too late. Once you get to Germany, Füssen to Rothenburg could be done with a €29 Bayern-Ticket (an all day pass for regional trains). Unless you are doing this on a weekend, you'll probable need a €48 QdL-Ticket from Rothenburg to Bacharach. You probably can't get to Haarlem without local transportation, which would be extra, but I do see Bacharach to Amsterdam for as low as €39 per person. So, what I am saying is that, except for Lauterbrunnen to Füssen, for which you have waited too long to get low fares, you can probably get better point-point fares in Germany, so limit your rail pass days.