Balaklava,
The Nemo Wide is a fine 3 gas dive computer that is more than enough for a diver starting his advanced nitrox/deco procedures with TDI. I used the same computer when I took those same classes and still use the Nemo Wide as my primary dive computer. That being said, you should not be counting on using any dive computer as the primary resource for decompression diving. In the TDI deco class you will learn to "cut tables", write them out on your slate (with additional tables for time over your dive plan) and then dive per your profile. Certainly the Nemo Wide (or any other dive computer) can be used to help with deco should you completly miss your planned profile. May I suggest that you look into decompression software such as GAP, V-Planner or iDeco?
With regards to a backup computer, I use another Nemo Wide. I chose that route because they both use the same software, computer model (RGBM) and I know that if one goes down, I will easily know how to use the other. That being said, even two computers positioned side by side may not read the same.
Regards,
Ltstanfo