Should I start seeing other people or just focus only on myself.
Seeing other people will only complicate things and distract you from working on you. Your time will be best spent focusing on yourself -- not your W, not another W, but you and your D.
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She took off her wedding rings. I can't find it in my heart to take mine off. I mean, we are still married. Should I take mine off?
Personal decision. Don't take them off in an attempt to spite her. If you are done and advertising to the world that you are not married, then take them off. If you are trying to save your M, then you still consider yourself married, right? Leave them on.