In the letter combination его the г is always pronounced this way. it is a historical spelling, at least that is what a site on the internet said (sorry I could not find the link to the site). therefore it is also pronounced this way in "Сегодня" as indicated by Mal-Tesers
"What is by him on dinner" is the literal translation. "у" is a preposition which means "by", but is used in some idiomatic expressions in Russian:
"X has Y" (to have something) is formed in Russian like "By X is Y".
"X is at Y's place" (to be at somebody else's house) is formed in Russian like "X is by Y".
Apart from this two idiomatic uses of "у" which Duolingo introduces quite early, preposition "у" can be used in the literal sense of "by" (to be by something), like "Я у школы", "I am by the school".