I assume Far East is still at that intersection. Great Chinese takeout.
I've never been to Far Eat, but it's likely Canadian Chinese food. It's not real Chinese food if they don't eat there
For real Chinese and other takeout, you have to go to the food court at Dixie Park Centre near Dixie and Eastgate Parkway. It's a non-descript building, but there are about 6 different places in there. It's a basic food court that won't win any decor awards. Most of the places have identical HK style street food, but there is a Chinese BBQ that hangs meat in the window, Filipino, Japanese, bubble tea and even a Gino's pizza.
It can get quite busy during the lunch hour because there's a Canada Post sorting facility nearby and it's close to the airport. There's even a dedicated area where vendors stack carboard boxes to be ready for party tray orders.
There's another good Chinese food court in the Mississauga Chinese Centre near Dundas and Dixie. That's the mall with the Chinese gate and dragon wall in it. The food court is in the same building as the supermarket.
AFAIK, the only Chinese food court left downtown is in the basement of the Chinatown Centre near Spadina and Dundas, but I'm sure it's quite run down these days.
Dragon City mall is also in the Spadina and Dundas area, but I don't think it ever had a food court. It does have a dim sum restaurant on the top floor, The Owl of Minerva for Korean, Juicy Dumpling, and a very small stall that sells bubble waffles too. There's also Pho Pasteur right next door.