Notes to Myself: Hearing Accents

A Japanese friend of mine met some of my foreign friends for the first time recently. The foreigners among the group, all native English speakers but from places with vastly different accents, tried a little Japanese here and there. After we had all parted my Japanese friend said that I sounded just like my other foreign friends when I speak Japanese - I was shocked. But, our accents our totally different, I pointed out. When we speak Japanese I can still hear an obviously American accent from my American friend, Australian accent from my Australian friend and so on.

So, then, does this mean that to many Japanese, we foreigners sound the same (if our native languages are the same)? Was it just her? My second question would be if we hear slightly different sets of sounds from the native speakers of the language we are trying to learn can we get closer to a native accent within a decent period of time? My thoughts move to language labs where I think you can see how well your voice patterns match recordings? I'd like to try something like that.