I was actually puzzled by the pronunciation of " עליו", in particular about the sound of "י", which I am used to associate to the sound 'ɪ' (like in 'hit') or 'i:' (like in 'see'). I am not much familiar with phonetic transcription, but I seem to hear something like /ɑ:lɑ:v/, while I would have expected either /ɑ:li:v/ or /ɑ:lɑ:i:v/. I guess it is the same (or similar) to "עכשיו", where I cannot hear the YOD. Is it correct to say that YOD is basically silent in " עליו" (or in "עכשיו")? Even with if I had נקודת to help me in the reading i would not know if I had to pronounce it at this point. Any rule? Or just learn the words and their pronunciation?
On the Pealim site, sweater, in Hebrew sveder, was written both as סוודר with no niqqud and סודר with niqqud. My guess is that in the first example, the double vav is a sign that it’s pronounced V and not wo or wu. In the second example, since the segol is on the vav, there’s no danger of the reader pronouncing the ו as wo or wu, so a single vav, rather than a double vav is okay.
It's not modern Hebrew, it's biblical: https://he.wikisource.org/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%91%D7%A8%D7%90%D7%A9%D7%99%D7%AA_%D7%9E%D7%98_%D7%9C%D7%92. I'm not sure what has happened here, and I wonder if the scholars have a good theory. I'm not very convinced by the differentiation hypothesis of Airelibre (are there other examples in the bible to such "unnatural" orthography to disambiguate?) If it were modern Hebrew writing, I'm sure עלוו and עכשוו would have worked great.
Call on/visit: לבקר
The other one, I think it's the same as "pick on" (maybe this is just a British usage, the most common meaning of "pick on" is obviously to do with being mean to someone). Anyway, essentially this is the same as "pick" or "choose", so I'd say:
The teacher called on her = המורה בחר/ה בה
I'm a native speaker, too. I agree that by the grammatical structure it fits the "about himself" meaning, like הוא נמצא אצלו בבית can perfectly mean "his own house". However, I don't agree it can really be interpreted this way. I don't think anyone would chose this to say "about himself", given the possibility to say על עצמו.