Recruiter initiated a hiring process while I was waiting their feedback for another role

Is this a common situation?

Unfortunately yes. Even "important" companies are sometimes very disorganized and data on the same candidate is not properly managed or shared. This can be good or bad for you, depending on how it plays out.

Can I rebound on this ?

Unlikely. Ironically you did the work that the recruiter should have been doing the first place and as a result they rejected you.

This is painful, but it's not necessarily a bad thing. Interviewing is NOT about "passing a test", it's about figuring out if the candidate is a good fit for the role and the company. It's frustrating, but often "No" is the correct answer. Hiring the wrong the person for the job will make everyone miserable including yourself. If you don't fit in there, you don't fit in there. Keep looking for place where you do !

Remember that the recruiter gets their commission only if the company hires you. A bad recruiter will be tempted to fire off buckshot applications in the hope that one of them hits the target.

You are in no way obligated to respond to any application that you did not approve, and it is legitimate to tell the company you didn't authorize that application so they know what to expect from this recruiter.

You might want to consider changing recruiters. If this happens again, I would.

Can I rebound on this and try to talk to the recruiter about the 3rd role she suggested or is it a sealed ?

In the US, if you fail an interview for a particular position, most companies will tell you to wait for about 6 months to 1 year before they will interview you again for a similar position. This is true for big software or IT companies. I assume that you apply for a software engineer position.

So, you can use this time frame to study and prepare well for the next interviews. Good luck.

Is this a common situation?

Yes.