Overall, I think folks have a good running list. I'm going to point out a few places where I've seen folks go wrong following rules like what you have articulated. Some of this is semantics, and I may be explaining what you already meant, but understand other people have different definitions for the words you use and thus would interpret the sometimes terse sentences differently...
I would add: Try not to just declare problems. Try to bring in potential solutions as well, especially if you are declaring the problem in public or to your manager. Note: This is related to attitude and being positive... but I'd note that being constructive and pointing out things that need to change and having ideas is not being negative. Some people think all conflict and all criticism is negative. Conflict can be healthy if it's on topic about the issue, and constructive criticism is necessary as well...
I'm then going to raise the stakes a bit on @Suze456's comment:
Check in with your managers periodically, make sure you have the same priorities.
...which is to say more broadly "learn to prioritize"
Don't go in and ask "what should I be doing". Go in with a list of things:
(1) Keep your boss up to date on things you are doing before he or she has to ask (as others have noted)
(2) Periodically (at each 1:1 you have) list the things people have asked you to do, but you don't think are top priorities and that you don't think you should be doing.
Only with #1 and #2 together, can you validate that you have the right priorities.
If you are off base with #2, your manager may know things you don't and can fill you in and help you change priorities.
#2 also lets them delegate that work to someone else on the team if appropriate, and doing it proactively before someone complains to them.
With #1 and #2 it also lets your manager defend you proactively if someone comes to push on them of why it wasn't done, because they know both what you are doing and that they agreed it wasn't your top priority.
#2 is at least equally important to #1 and forgotten by many, many people.
I'd also add to the list
(3) When necessary, talk about places where you specifically "need help" and be prepared to talk through what you need to learn or how they can help you reach out to the right people or whatever... don't be afraid to periodically give them work to do if it's helping you move your project forward and appropriate for them do to either for your development or because it's a cross team interaction that can't be agreed upon at your level (because it involves budget changes or whatever)
Then a few comments:
Don't blab confidential/sensitive stuff
...and to double down on this, if you discover a confidential project (or what some might refer to as a non-disclosure project) exists (these usually have code names associated with them), don't ask anyone about it. If someone starts talking too much about it, politely point out you are not disclosed to it, and change the subject or move out of that conversation. Also, don't ask to be added to the project. Leave it alone, and it will find you if you need to be included. The more you try to get on such projects, the less they will find you.
* Punctuality (showing up to work, email responses)
The first part I get. Early on it's probably better for you to arrive before your boss and leave after, if just for the perception value.
I have to say the latter part of this makes me nervous, because "punctual" is relative and can be misunderstood. (e.g. My mom's definition of punctual and my dad's definition of "punctual" are VERY different)
It is distinctly possible e-mail rapidly becomes overwhelming, but keep in mind e-mail is (likely) not your job. I'd set aside time each day to deal with it, but don't feel when an e-mail comes in you have to reply immediately. First, it can (falsely) give an impression you have nothing to do. If it happens all the time, it demonstrates you are prioritizing e-mail, and you should seriously ask whether that should be first on the list... (hint: usually no) ...to be literal, it's the "on schedule" part of punctual, not the "prompt" part of punctual that is important...
Again @Suze456 is right on: The key is to keep any commitments you make. In my experience, consistency about keeping commitments is far, far more important than being quick with responses. Also learn what e-mails are important to respond to quickly. When a sales team asks a question, get on it, because you are likely in the critical path of revenue. If someone asks for status on a lower priority item, it can probably live for a few days if other things are critical... note again how this comes back to learning prioritization (and being "on schedule")...
Last, but certainly not least: Do the right thing. This is much more than a moral/ethical statement, although that is the place to start. As you get the rest of the items from this list you are generating mastered (and as you learn about the company's eventual goals): Don't think one step out about what you can achieve. Think strategically about what is the right thing to do, then define the tactical steps to get to the right thing. Don't compromise with yourself, communicate with management and make them put the plan back into a budgetary or other box. You can't be insane about fighting only for the strategic, but the higher "band" employees must think strategically... and sometimes have to be asking for the $ and resources to do the right thing and cause lots and lots of discomfort for the company.