"I know everything about that man."
Translation:O tamhletom muži vím všechno.
Approximate analogies of Czech demonstratives with English:
O tom muži - about the/that man
O tamtom muži - about that man there
O tamhletom muži - about that man over there
O tomto muži - about this man (formally)
O tomhle muži - about this man
O tomhletom muži - about this man here
And then there are also several dialectal versions like "o tadytom", "o tutom", "o hentom", "o tomdlectom", "o támletom" etc. :)
The babička sentence is a gray area. "O svých babičkách víme málo" is much better, even though "známe" is acceptable there.
We normally say "vím všechno" (I know everything) and "nevím nic" (I know nothing) but "znám všechny" (I know everybody) and "neznám nikoho" (I don't know anybody).
So... "Znám toho muže velmi dobře." but "Vím o něm všechno." - you see how the first one, "znát" expresses familiarity, actual connection with the man, while the second sentence with "vědět" talks about information - I may know details about his life but that doesn't necessarily mean I know him personally on a human level. Hope this helps.