For growth chart you can try glow baby app. If you pay to get their premium you can record teething and even see the chart for activity (tummy time, outdoor play; like how long, etc). For vaccination, see this website. https://www.healthhub.sg/live-healthy/363/immunisation_chart_based_on_age
Usually pd or polyclinic will tell you when’s your child next immunisation. Mani and pedi routine is depending on your child. Cut it when it’s long. For my baby, I cut her fingernails around once every 3 days while her toes nail as it’s not growing fast can cut around once every 2 weeks. From here just make it a routine for yourself and you will surely rmb.