I'm not sure about activity points but thought it was 12 a week same as on points. Lydia's your expert on that one.
Chinese-wise, I'd always go for a chow mein. I'd have a mushroom one but I'm veggie anyway. Chicken or prawns are core foods though and so are noodles so she'd probably only need to count a couple of points for the oil.
Technically if you are eating more than 2 non core ingredients in a meal then you are supposed to point the whole meal, but in reality very few people do that and the majority only point the non core items ie oil - which seems sensible to me. Hope you mum enjoyed the chinese.
As for activity points WW changed the rules on this about a year ago and you can now eat as many of your activity points as you want (or as few).
I'm a vegetarian but if I have veggie gravy when I was on Core I always pointed it as its a processed food so I would point it at 1/2 point per 75g serving. Although if you make your own gravy from scratch then I can't see why that can't be Core and just point the thickening agents if you use any.
Oh, I only asked about that food, because both the gravey and the beef slices are core. But this is a pack from Tesco with both foods in, so wondered if its a bend of the core rules?