Ok, with so much misinformation out in our big wide world, The Balance Guy will set you straight.
1. Elimination diets don't work. In my experience this just makes you want it more. You need wiggle room.
2. Women can lift heavy... if they want too. Women will not bulk up because they lack the testosterone to build large amounts of muscle.
3. All cardiovascular exercise has health benefits. Just choose your favorite activity and go for it. You will stuck with this in the long term. Don't let anybody tell you different.