I'm pretty surprised to see so many people recommending post it notes or a whiteboard. Even if you aren't remote, people are going to have sick days or WFH days

I'm pretty surprised to see so many people recommending post it notes or a whiteboard. Even if you aren't remote, people are going to have sick days or WFH days and "can you take a picture of the whiteboard for me" requests are nonsensical. Start with Trello. You can easily bend Trello to work with any productivity/PM system. Easy to get started and easy to evolve your process over time. Lots of great examples of how people are using it and some cool plugins to extend it. #1 is extremely easy to implement in Trello. #3 is definitely possible but takes some time and buy in.