The steps of replacing a Fabric Interconnect are detailed in the docs:
+ https://www.cisco.com/c/en/us/td/docs/unified_computing/ucs/hw/6200-install-guide/6200_HIG/6200_HIG_chapter_010.html#task_3DEE03FA10DC41A68FBB458567849184
To answer your questions. . .
Most often when a FI fails there will be a service disruption, but that is usually brief as the redundant working side will take over.
Yes faults may occur during the synchronization process as the replacement may show "hardware failure" (or whatever the failed FI had) while the device is coming up and not fully sync'd but those faults should clear as the replacement is found to NOT really have those faults.
I would shut the failed FI uplinks upstream to prevent the replacement FI from being in the data path until the replacement has rejoined the HA cluster and fully ready. Once you are satisfied the replacement is working and upgraded and sync'd and happy then you can re-enable the upstream links to allow traffic.