I agree with Bertie... strength training might not help you lose weight quickly, but it will help you
look and
feel better in the short term, and you'll probably lose the weight more easily long term... all of which are much more important than the # you see on the scale 7 weeks from now, IMO.
Adding strength training to that schedule would probably lead to being pretty tired out... so maybe less days of biking or other strenuous activities. The walk with your mom sounds like a pretty light workout for you, so I see no reason you couldn't do it almost every day.
Congrats on the internship!!! I know what you mean about using your free time wisely before you go. In exactly 2 weeks I'll be done with my degree, and I'm starting a PhD program in late August, so until then I plan on just working part time (20 hours a week) and putting lots more effort into losing weight and getting healthier. Let us know how it goes!