It should be:
Now that I think about it, it was from that moment that I started to have doubts about him.
It sounds a bit awkward with all those thats, but "that" is grammatically correct. It might read better this way:
Now that I think about it, that was the moment when I started to have doubts about him.
Or better yet:
That was the moment when I started to doubt him.
I'm not sure if where or when would be incorrect grammatically speaking, but either would be confusingly redundant, as they serve essentially the same purpose as the prepositional phrase from that moment -- i.e., to specify a point in time. Thus, if I hear the sentence with either when or where in the place of that, it sets an expectation that it refers to yet another point in time at which something else happened after you started to have doubts, e.g.:
...it was from that moment when I started to have doubts about him that I began trying to hack into his e-mail account to see if he was cheating.
In short, if you use when or where, the thought feels unfinished to this American English speaker.
That, on the other hand, serves as a conjunction introducing the subordinate clause "I started to have doubts about him." Thus, it completes a thought.
You could use either in this instance, but "leave" is the more accurate term of the two: "Go" refers to the whole journey whereas "leave" is the act of moving away from the current location - the beginning of the journey.
Best Answer
They are very different constructions, though both are (probably) possible here.
First, note that stop, like many verbs denoting a change of state, can be used both transitively and intransitively:
The transitive use usually implies that the stopping was caused by something external, whereas the intransitive use does not.
The transitive use, like any transitive verb, can be made passive:
As usual for a passive, the agent is optional; but "The ball was stopped" implies an external agent, unlike "the ball stopped".
We would not normally talk about a match stopping without an external agent:
but
is dubious. We'd normally used a word like "finished" or "ended"; and any other way it stopped would be from an external cause.
Now, what about "has stopped"?
"Has" + past participle is how we form the present perfect, of the active verb. So "The match has stopped" is very like "The match stopped" (intransitive), but with a perfect instead of a simple past. Perfect is used when the speaker wants to express that an event in the past has some present relevance.
I think that (leaving aside the unlikelihood of talking about a match stopping without external influence, as I discussed above), the present perfect is much less likely here than the simple past "from where it stopped"; but it is possible.