Duolingo course is really a scramble of both. To add pepper to the wound, the audio recordings are not correct in like 50% of times (they depend on text-to-speech machine which is not standardized for Arabic).
This said, the word عند does mean (at) and (has). However, there is another word which means (has) in Arabic but I didn't see Duolingo using it so far, and that is لدى (ladá).
Forget about the markings on Duolingo. It's a mess.
The sentence above should sound like: 3inda joodee baytun jadeed(un).
The audio for this course (and some others) is generated by a speech machine which has a lot of mistakes, beside other issues with this course specifically mixing standard and dialect.
Anyway, marking a "mute" consonant with sukun (the circle above the letter) is a general sign and can occur at any position in the word. Worth noting that when we write in day-to-day usage, we don't really use these signs. We just know how to read like that. These diacritics or vowel markers are put here in this course as a guide for new-comers.
Now, I don't want to delve deep into grammar here but the word بيت above, should be (baytun) and not (bayt) as the audio is saying. And to write it in a correct way with all the characters it should look something like that:
That's (baytun). The last marker on (t) is Tanwin (Tanwin bil-Dham), and it is spelled as (-un). It's a long story why this is here but as I said I don't want to get into grammar just yet.
Best of luck. Duo can be a good starting point but definitely that "scholar"
On youtube there are some people out there also that teach some stuff (either dialect or standard). They can be a good source as well - but if you are looking for standard Arabic, stay away from people who say that it's OK to say ج (J) as (G) or (Zh); This is not a thing even. This letter should (in standard Arabic) sound like (J) in English (or Ge/Gi in Italian).
so so - it depends on the situation really.
Did she buy the house? Then you say اشترت (ištarat: she bought)
Did she "gain" the house in some way? then you might say حصلت على (Hacalat 3alá: gained).
Did she inherit the house? You might say then ورثت (waraþat: she inherited).
So what the sentence above says is just, "she has a new house" that's all