Marina, Grow roots in a NEW apartment? It doesn't make much sense. It takes time to grow roots. I think the proper expression is " to put down roots" which means to begin to grow roots. Other possibilities: "settle INTO a new apartment" .... "settle into".... get comfortable in a new place or situation or maybe something more general like: "get used to living in a/the new apartment" "adjust to life in a/the new apartment"

In English there is a phrasal verb, 'to settle in'. To settle in to your new flat / apartment is more or less the same as making yourself comfortable in your new flat / apartment / home. This is slightly different to 'settling' in the country, which is a way of saying that the country has become your home, not necessarily that you are comfortable!

Правильно, но звучит немного bookish, наверно проще сказать settled For ex : a family long settled in the country семья, давно живущая в этой стране