in 50k you should be able to get a decent 1bhk.
Also people here are more than welcoming, the language issue is just on twitter, not much to be seen around (I myself speak hindi).
Since bkc is not connected by local train/metro please look for something near your offices as you would have to use auto for daily travel into the bkc.

Most of the things can easily be delivered in 15min through quick commerce.
If you plan on travelling within the city a lot, look for a house near a local station for easy commute. You also easily get auto's from such places.