I also added birthdays to the contacts on my phone. I found an Android app called Birday that reminds me when someone’s birthday is based on the dates in my contacts. Birday and the clock are the only two widgets on my homescreen. People seem to like that I reach out with a text or phone call to talk to them on their birthday over the FB “click to send happy birthday” thing (which is still better than forgetting, to be fair).
Yes, works well for me. My work uses GMail and K-9 supports it. I don’t have the Play Store and K-9 supports OAuth.