Some dictionaries can be confusing. A little trick,if you use Google Chrome or set your browser to set Google to be your default search engine, type "define ..." What ever you need help with will be defined for you. From Google Search: prop•er ˈpräpər/ adjective 1. truly what something is said or regarded to be; genuine. "she's never had a proper job" synonyms: real, genuine, actual, true, bona fide; "he's not a proper scientist" 2. of the required type; suitable or appropriate. "an artist needs the proper tools" synonyms: right, correct, accepted, orthodox,conventional, established, official,formal, regular, acceptable,appropriate, de rigueur; archaicmeet "the proper channels" 3. adverb BRITISHinformaldialect satisfactorily or correctly. "my eyes were all blurry and I couldn't see proper" the part of a church service that varies with the season or festival.

Not any more. The Latin root of 'proper' does mean 'own', and if you are reading English texts that are several hundred years old, you may come across the word used in this older sense. This meaning persists today in words such as 'property' . However, the meaning has changed over the centuries, and 'proper' in modern day English means correct/real/acceptable.

No, you wouldn't say it--you'd say "it's his own home." I know that "proprio" in Italian can be used in this way, but I've never heard it said in English.