as i know when using "Possessive adjective" not as subject of a sentence the following noun should not take the "possessive suffixes" (at least it is better not to take);
benim evim burada. (benim evim==subject) (My house is here)
benim evi gormelisin. (benim ev==direct object) (You need to see my house)
but also when using as subject in colloquial language you may omit the suffix ;
bizim yazlık şahane! (our cottage is great!)
Mizinamo, I think that too, but English is not my mother language. I understood the sentence in a different way. I don't know how to explain. I think if you make 2 sentences of the Turkish one you would get: "Bizim haber ver. = Let us know" and as subordinary clause "eve varirsa" = If he arrives at the house (our > only implied because of "let US know") Therefore we could think that "bizim eve means our house", but that would be bizim evimiz in another sentence without subordinary clause. The Turkish people usually do not double the things: Onlar yer ya da Yerler, but not Onlar yerler. I think that in this sentence the same happened with house.
If the course contributors are going to introduce colloquial usage that doesn't match anything taught in the course so far, they really should explain it in the Tips section, otherwise it just confuses, frustrates and demotivates a lot of students who have no way of knowing why the grammar they've been consistently drilled on for so long no longer applies.
It sounds weird because it puts too much stress on the fact that the home belongs to us. 'Bizim' alone is sufficent to indicate whose home is it, so if you add an optional '-imiz' it sounds a little bit pretentious (not too much). Though there are some situations where it sounds normal.
"bizim evimize.." is correct. Depending on who you ask, people say it may sound strange to a native because of the duplication of "our". For short, people in everyday communication say "Bizim eve..." a lot, or "Evimize..." (without the bizim). But it is correct grammar.
Here's what I have understood from Duolingo lessons. Var- is the root (varmak - to arrive), -ır- is the tense sign for aorist ("varmak" is an irregular verb), -sa means "if". An aorist tense personal ending should be after -sa, its absence means that the verb is in the 3rd person singular. So, "varırsa" = if he arrives.