M.R.
I second the advice to either join a gym, get a few sessions with a personal trainer, or take some classes that will get you acquainted with what you need to do to reach your individual goals.
1 - yes you need to add squats and lunges for your legs. These are known as functional exercises - every time you sit down and get back up you're doing part of a squat. Every time you lunge to the left or the right to pick up something, including your child, off of the floor you're doing a lunge.
2 - arm exercises: be sure to work the biceps, triceps, and deltoids. A simple rotation would be bicep curls, tricep extensions, and t-raises for shoulders.
3 - you're missing several other major muscle groups. Your major muscle groups include pectorals (chest), latissimus dorsi (back), and your lower body (gluteus maximus, quadriceps, hamstrings). For chest, do any sort of exercise that is a 'push' exercise. For back, do any sort of exercise that is a 'pull' exercise. For the lower body do your squats and lunges. Be sure to also do core work which includes the following: abdominus rectus, obliques, transverse, erector spinae, among others. Many people make the mistake of doing crunches until the cows come home but forget to do lower back exercises. Do both to keep it in balance.
Feel free to send me a PM if you have questions or want further suggestions.