
Samsung Galaxy Note 10.1
The latest firmware for Samsung Galaxy Note 10.1 (SM-P605L) is P605LKLUCQA2 with Android 4.4.2, released on January 19, 2017 for 1 region (CSC). Every official firmware build for SM-P605L, 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/P605LKLUCQA2
Specifications of SM-P605, a regional variant of the same device. Chipset and SIM lines are left out: they can differ by region.

SM-P580X

SM-P610X

SM-P620

SM-P605V

SM-P605K

SM-P625

SM-P907A

SM-P905V
You can find the firmware on the model: SM-P605L page.
Yes, all firmware files for SM-P605L are 100% official, original, and obtained directly from Samsung servers.
To flash SM-P605L, 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 SM-P605L.