In all the daily prayers we say Kriat Shema except Minchah. This is my understanding of why we do not say this is because at the beginning of Minchah we are bringing our offerings of korbanot and keterot as if we are in Beit Hamikdash. Am I understanding this correctly?
Also haven’t we fulfilled our daily obligation by saying the Shema once in the morning and once at night. Is the reason for us saying Kriat Shema in all the other prayers minus Minchah is to say them with a Minyan?
Keriat Shema is recited twice a day, in accordance with the Torah mitzvah to recite the Shema morning and evening. Chazal enacted that it should be part of the prayer service, ensuring that the Redemption from Egypt, which is mentioned at the end of the Shema and in the beracha that follows it, will be mentioned just before the Shemoneh Esrei prayer.
The times for the recitation of the Shema are morning and evening, but not afternoon, and this is the reason why there is no recitation of Shema in the Mincha prayer.
Somebody who says Shema outside the framework of the prayers (for instance, if Shacharit is davened too late for the morning Shema), recites Shema again as part of the Shacharit prayer, which ensures that he approximates the Redemption to the prayer of Shemoneh Esrei.