I heard that you have to or should say shema and Shemoneh Esrei with the minyan. what teffilos can you skip in order to catch up and be able to say Shema and Shemoneh Esrei with the minyan? Also can one go back and say those tefilos that were skipped after davening?
Shalom, Thank you for your question. It is great to see that praying with a minyan is important to you - may you be blessed that all your prayers are heard together with the prayers of the whole of the Jewish people. Of course one should try to get to the minyan on time so that you can pray everything in the correct order with the minyan. However, sometimes this doesn't happen, and one arrives late. In such a situation, the main thing is to try and say the Amidah with the minyan (one does not have to say shema with a minyan). One can skip over parts of the prayers to get to the Amidah with the minyan. The minimum you need to do is put on tallit and tefillin, and say asher yatzar, al netilat yadayim, Elokai neshama and the blessing over the Torah. Then say baruch she'amar, ashray, [nishmat on Shabbat] and yishtabach, and then say everything from barechu until the Amidah. Hopefully this will get you to the Amidah with the minyan. But if not, one could say the Amidah together with the chazan in his repetition (saying everything he says, including the kedusha, word for word with him). After the service ends, you then go back and complete the parts you missed. It is quite possible that you (or your synagogue) have an Artscroll siddur. If so, you may want to look in the back where there is a nice summary of all these laws in English (and many more). Blessings.