Yes, if you have been following Rajan's morning meditation sessions, that is the essence of meditation. You may very well follow the same pattern on your own too. Seasoned mediators may achieve that kind of mental strength and a permanent state where it is not easy to disturb their equanimity.
Simply put meditation is an art of bringing focus and awareness on the present without being overly affected by the past or future as that's where for majority of us our mind tends to operate. It's extremely unlikely one would ever achieve a state of absolute equanimity in a normal life.
What meditation will help you is in becoming highly resilient, focus on what you can control and provide you with mental focus skills even during the most daunting times.
You can definitely meditate on your own. Beginner meditators often think that meditation is about attaining some blissful state where the mind does not wander at all and we become immune to stress and pain. This is a fantasy. The truth is that everyone's mind wanders - because that is the nature of the mind. As long as you are able to keep bringing your mind back to the object of meditation (the breath, in the meditation practice that we do), you are doing just fine. At this stage of your meditation practice, don't aim too high for a "state where nothing affects us." It's an impossible state.
Equanimity is not about not letting anything affect us. It is about how even-minded we can be towards the emotions and situations that arise in our lives. In a stressful or sad situation, you may still feel stressed/sad, but equanimity is the ability to maintain a balanced mind even amidst that chaos. It is different from "not letting anything affect us."
Equanimity is not indifference or apathy. It's an even-minded approach towards all experiences, regardless of whether they feel pleasant, unpleasant, or neutral.
Continue meditating even through the frustrations. Everyone feels them. Cultivating equanimity is a more advanced practice. Stay steady and on the path. You'll get there.