I think that the solution which is marked "best" should use "see" rather than "looking at", though. "Looking at" can be an alternative translation if you think that is an acceptable translation. (It seems wrong to me.)
If I remember right the (main) translation originally was the professor is looking at the sun, and this is what Lena's and Mizinamo's comments are about. In response to this discussion the translation was then changed to the present one.
As a translation, no. You are also correct. Just keep in mind that in greek there's no difference between looking at something which is steady and something that is moving in everyday speech. Also the immediate translation of "watch" is παρακολουθώ
Not quite the same word.
The gas is ήλιο in modern Greek, and the Ancient Greek form would have been ήλιον. It's a neuter noun (modern το ήλιο, ancient το ήλιον).
If the Romans had borrowed the word, it would have been helium, using the Latin ending for a neuter second-declension noun -- and that is the form we use in English, as newly-coined Greek words are often put into English as if they had come through Latin.
The noun looks similar to the accusative case of the masculine noun ο ήλιος (the sun): modern τον ήλιο, ancient τον ήλιον.
But they're not the same word -- helium is derived from ήλιος with the -ium ending used for the names of metals, since that's what scientists originally believed it was (see https://www.etymonline.com/word/-ium and https://www.etymonline.com/word/helium ).