Wij hebben een huis gekocht

To an English speaker "we bought a home" sounds like "we bought a house."

British estate agents certainly advertise "Homes for sale". It is a usage I hate, because a home is also a synonym for institutional care, as you can see in sentences like "When her parents were both killed in an accident, she was sent to a home"; "When she was too old to care for herself, we put her in a home." To me "home" is the place you feel comfortable living in, be it a building or the town or country you came from. As some people say, "Builders can build a house, but only the people living in it can make it a home." When I bought my first residential property (which was by chance a house), I was thus annoyed at people who said I had bought a "home". It was not home at all for quite a long time. So, for me, "a home" is not a happy usage for "a house or a flat or a static caravan or...".

"When her parents were both killed in an accident, she was sent to a home"; "When she was too old to care for herself, we put her in a home."

"A home" without a qualifier sounds British and a bit archaic to me. I'd expect a qualifier. "Nursing home" would probably be the most common. Maybe "retirement home." A Children's Receiving Home is a place that gives emergency`shelter to children removed from abusive situations. "Rest home" and "old folks home" are out-of-date.

(I did once read about a Home for Hopeless Inebriates in a murder mystery from the 1930s.)

Is "homely" still a compliment in British English or is it, too, out-of-date?

Is "homely" still a compliment in British English or is it, too, out-of-date?

As far as I am aware "homely" still means "welcoming and comfortable" here. Unfortunately translators of Tolkien have sometimes misunderstood his Last Homely House at Rivendell, though you wonder how they could possibly have translated it with the American meaning and not wondered at what a very odd thing that is to call it.

In Dutch there is no distinction between 'home' and 'house'. Both are called huis, sometimes with a t in front: thuis (I'm home - Ik ben thuis). Any type of living space is called huis, but we do have different words for different types of houses.

OPs reaction to the new house is similar to the reaction of my Australian cousin to my house. She said: O, what a lovely little unit, while I live in a house which -by Dutch standards of course- is actually big enough to accommodate a family of 5.

In Spanish the usage is similar to French. If you say "compré una casa" it means you bought a house (not an apartment); but if you're going home you would say "me voy a casa", whether you live in a house or an apartment.