Summary: Staying positive, energetic, open-minded, and friendly will help ensure your first day of work at a new job is not also your last.
The first day of a new job will lay the stones for how the job will go. Do or say the wrong things on your first day and your colleagues might dislike you or even cause you to lose your job.
Start your new job with energy and humility. Coming off as a know-it-all won't win anyone over.
Do we even have to explain why saying this on your first day is beyond inappropriate?
You should have already discussed this before your first day of work. Making these kinds of announcements shows you are not committed to the job.
Being accessible to your new boss is the most important part of your first few days and weeks. Paperwork can be done during other times when there is nothing for you to do.
With this question you are asking coworkers to gossip, which is a big no-no. Coworkers may have issues with each other that have nothing to do with you.
Asking questions that deal with money before actually asking questions that relate to your job give the wrong impression. Being engaged in the job and not the paycheck if you want to make sure the paychecks keep coming.