1.Is 'Neither of them could speak Englihs.' different
from 'Both of them couldn't speak English.'?

2. Does 'I don't know both of them.'mean 'I don't know any of them.'?

============1.Is 'Neither of them could speak Englihs.' different from 'Both of them couldn't speak English.'?

THESE MEAN THE SAME. THEY BOTH IMPLY TWO PEOPLE COULD NOT SPEAK ENGLISH.

=============2. Does 'I don't know both of them.'mean 'I don't know any of them.'?

IT COULD, BUT 'BOTH' IMPLIES 'TWO'; WHEREAS 'ANY' DOES NOT. 'ANY' COULD BE MORE THAN TWO.