
Samsung Galaxy Note
The latest firmware for Samsung Galaxy Note (GT-N7005) is N7005DXMC1 with Android 4.0.4 (Ice Cream Sandwich), released on March 11, 2013 for 4 regions (CSC). Every official firmware build for GT-N7005, 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/N7005DXMC1

GT-N7000B

GT-N5105

GT-N8020

GT-N8013

GT-N8010

GT-N8005

GT-N8000

GT-N7108D
You can find the firmware on the model: GT-N7005 page.
Yes, all firmware files for GT-N7005 are 100% official, original, and obtained directly from Samsung servers.
To flash GT-N7005, 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 GT-N7005.