Well, Tatiana's writing can be hard to read, but I can definately make out the 'ья' in her signature.
Ferah, do you mean that he signed 'Nicolai' when writing in English/French etc. and not Russian?? 'Cause there's no such c in Russian (what looks like a с is actually an s) Perhaps he just put in a c to make it more... latinized... (if that's even a word, LOL) But I would say that it is more correctly transliterated as a k (espeically because the English c has different sounds, some of which are not the same as the Russian к)
So I guess you could argue for Nicolaevna/Nicolaevich as a patronymic.
'Nicholaievna' as a patronymic is wrong. Nikolai doesn't have a 'ch' in it, but besides: when forming a patronymic for a child, whose father's name ends in a vowel and й, like Николай and Алексей, you have to drop the й and add евич/евна. So there should NEVER be an i (й) there.