The latest firmware for SCH-R830C is R830CVVAMI4 with Android 4.1.2 (Jelly Bean), released on October 7, 2013 for 1 region (CSC). Every official firmware build for SCH-R830C, newest first: one row per build with all regions (CSC) that received it.
Each firmware build has its own page at https://samfirm.shop/build/{PDA}, where {PDA} is the build number from the list above. Example: https://samfirm.shop/build/R830CVVAMI4

SCH-R970X

SCH-L710

SCH-I939D

SCH-I545PP

SCH-I545L

SCH-I435

SCH-I545

SCH-P709
You can find the firmware on the model: SCH-R830C page.
Yes, all firmware files for SCH-R830C are 100% official, original, and obtained directly from Samsung servers.
To flash SCH-R830C, you need to download the appropriate firmware, put your device into Download Mode, and use the Odin tool to load the BL, AP, CP, and CSC files.
Downgrading is only possible if the bootloader version (binary bit) of the old firmware matches the current one. Always check the binary version before flashing SCH-R830C.