how were copies of vinyl made in "third-party" countries

...and the entire mastering to lacquer might take place at each pressing plant, or just some pressing plants. Again, depends.

A lot depended on how many units they thought would sell. If caught short they may run the stampers longer or make new masters.

is there a way to tell if an LP is likely to sound better from looking at it? 

The answer is no but I always looked for coarse grooves. That shows they were changing the pitch for more dynamic range but there are good sounding records that show even spacing also. 

My wife being a professor of German history means we spend a lot of time in Berlin.  Love buying DDR records like on the Amiga and Eterna labels.  Not the best SQ but fun to see what they allowed.

To add a bit to the cacophony, in the 60s, 70s, and 80s, where you sometimes had the same performance available on Decca, London, and/or Angel labels, one always knew to seek out the British pressing over the US pressing. Same went for EMI vs Capitol.

I know a lot of audiophiles in Hungary, they swear by US LPs and CDs as if God created them. The grass is always greaner....

and I just looked: my 90s Hungarian LPs are absolute crap while 70s and 80s are delightful. So much for capitalism :)