When davening with a minyan I understand it’s customary to keep up with the congregation even if you don’t pray as fast as others by starting each new prayer or psalm when the others do even if you aren’t able to finish the last one (except for the Shemoneh Esrae and the three blessings of the Shema). If this is correct, where does the Halacha come from and where may I read more about it? Thank you!

ב"ה Shalom The main purpose of davening with a minyan is to say the Shmoneh Esreh with a minyan. Mishnah Berurah (90:28). If one comes to shul late or davens slow and wants to catch up the laws of "skipping" Pesukei d'zimra and what parts have priority are found in the Shulchan Aruch Orach Chaim 52. As far as reading more about it you can probably find some good material on the internet just by searching for "catching up with davening". However, if you want to treat yourself to a real in-depth book, I suggest getting "The World of Prayer " by Rabbi Dr. Elie Munk zt"l originally written in German in 1933 and then published in English in 1953. Many years ago, I received it for my Bar Mitzvah, but I was unable to appreciate it until I was older and I am indebted to those who brought this most important book to my attention. Gmar Chatima tova.