Should I do core exercises? Strength training advice?

It's not about the calories burned it's about improving fitness, right? Cause doing 10 minutes of core workouts won't burn a ton of calories. I've been losing weight over a long period of time and have been jogging and walking a lot but mostly watching what I eat. My doc said that I should add strength because as you age you lose muscle mass. I started lifting these little 5 lb weights I found about 45 times with a little break between each 15 doing different types of lifting (like 45 times for each lifting move) and downloaded an ab app and have been doing it. Do you think when the rest of the fat comes off there will be a difference? Am I doing ok incorporating strength training? The app is called "ab workout" and has good reviews.