My answer describes the chain I work for, in my specific area/region:
Short answer: No, everything you mentioned does not matter when you are an intern.
Long answer: No, again, all that stuff you mentioned does not matter as an intern. The chain does not track registration of emails, errors made in data entry, flavoring of Rx's, or any other thing you do as an intern.
Corporate only cares about store performance and RPh performance. What you do as an intern doesn't matter to them at all. Why does corporate like interns? You are like an RPh, can do everything an RPh does, and corporate pays a fraction of the cost of an RPh. Now, when does being an intern actually matter? When the transition of going from intern to RPh for the company occurs. This will happen when they begin interviewing interns for RPh positions, usually in the 5th or 6th year of pharmacy school (or 3rd or 4th year in a four year school). After they interview you, they have a good idea if they want you or not. They will straight out tell you if they want you or not. This is done by offering you a position, and you must commit. If you don't commit, then you have up to a certain date to work for the company, then you have to leave. Now, after your interview, that's when you start proactively working more hours in the district and in busier stores like 24 hour stores, and that's when you email the Rx supervisor and ask them to place you in stores during your breaks (winter breaks, spring breaks, etc), rotations, months off, etc. Once they see that you are working more and more for them in your 6th year and want to be a part of the company, they start caring about you and once you become an RPh, that's when your performance is looked at.
Once again, that's how it was for me in the chain I work for.