Another related question; how exactly were armoured trains used in combat? Was their role similar to the tanks that came later on (railway lines permitting), or were they used differently?
I ask specifically about armoured trains because I am not aware of any other armoured land vehicles prior to the introduction of tanks (EDIT: apart from armoured cars, but they don't fill the same role as tanks).
For your secondary questions, this old post should cover them pretty well, but for your main question, while I haven't read much to suggest a direct genesis (the roles were very different, to say the least), I can't say with absolute authority just how little influence there was, so someone who can speak to the early development of the Mark I would be better to weigh in here. The most I can say is that the British Navy, due to some weird circumstances, oversaw much of the British work with Armored Trains, and the Navy also was instrumental in developing the Tank, so they aren't not related at all.