Hi! The first is more natural because you're focussing on your current state. You might add the word still if you wanted to emphasise that it's been a long time. For example, "I'm still single after breaking up with Tom last year." For the present perfect, we'd usually add a time duration. For example, "I've been single for a year now after I broke up with Tom." Hope this helps!

Both are fine. It depends what you want to emphasize: "I am single" reveals your state right now. "I have been single" describes your current *experience* of being single. "Since" would be better than "after".

“I’m single, having broken up with Tom last year” would sound more natural, and how a native speaker would say it.