近如 in Vietnamese, 近乎 in Chinese
Technically yes but then again not quite! 近 in standard Sino-Vietnamese is cận while gần, although most likely from the same origin, was borrowed much earlier on.
perhaps it was similar to 家 ("gia" vs "nhà")
There is actually another debated origin of that word coming from 庌 which means something like a house on a cliff. Nha is similar to nhà and the meaning + the semantic component is somewhat of a match.
Where do you find this profound information? Wiktionary doesn't have much info.
I am also interested in words' origins of a language.