This is really two questions I think. The page you want to see about adding speed limits is [Key:maxspeed][1] and roads already tagged can be reviewed on [this map][2] (I believe others are also available).
I don't know the answer to your NMEA question - if it is speed related won't it contain the speed you were actually going rather than the speed limit?
limit? The [NMEA][3] wiki page suggests traces can be opened in JOSM though, if that helps.
[1]: http://wiki.openstreetmap.org/wiki/Key:maxspeed
[2]: http://www.itoworld.com/map/124?lon=1.17775&lat=52.05264&zoom=12http://www.itoworld.com/map/124?lon=1.17775&lat=52.05264&zoom=12
[3]: http://wiki.openstreetmap.org/wiki/NMEA