> Should I poll my supervisor/co-worker about every problem to see if there is already a solution? As the new guy, I have no idea who or what I should poll people about.

It helps to have a company culture that encourages openness and asking questions. My current company goes so far as to have a Slack channel, #askanything, where folks can ask anything. We'd much rather you ask early in the development process than pursue a path that will lead to duplication.