Congratulations on interviewing! Partners can sometimes be wildcards in the interview process, and you need to be seriously considered as a candidate by the company for them to ask a partner to take time out of their day to interview.
That said, each firm/company has different interviewing methods. If you know someone else in the company, it might be more helpful for them to provide their opinion, but my interpretation is:
- I wouldn't read too much into him holding his phone. Frankly, partners are always multitasking because they have multiple clients and projects at a time – they need to have a pulse on whatever is going on.
- It's great that you caught the mistakes when being guided. It shows you have potential to be coached, which companies are looking for. I wouldn't worry; after all, I also made silly math mistakes in every single one of my McKinsey interviews (and still got the offer!).
- The partner's time is very valuable and they know it. If they did not have interest in advancing you, they would not need to ask you about your expected salary and notice period. They could have just finished the interview then and there and thanked you for your time.
The signs seem positive to me, but again, lots could go into your evaluation (including your expected salary and notice response). Don't lose sleep over this – you already did your best, and that's what matters.