At the end of Back to the Future, Part III, Marty declines to enter the drag race that was shown in the previous film to have disastrous consequences for his musical career. The 2015 fax of future-Marty being fired is now blank, implying that the future of the McFlys shown in Part II no longer exists. So, did Marty just erase his two children from the timeline?
The movie never says specifically, but it may have been mentioned in the animated series. Marty declines to race against Needles, which did change the future. Marty and Jennifer's future did change after this event, but this was for the better.
Marty's involvement in the race had very negative consequences to his future life. He breaks his arm, and gives up his possible music career. In the events in BTTF 2, Marty and Jennifer were not very happy, or successful people. Many of his ills came directly from the race. Their kids were trouble makers, they had financial issues, etc. Marty and Jennifer also were married at the Chapel O' Love instead of having a big wedding.
It is likely that Marty and Jennifer did get married, and still have children just like his parents did. In the first BTTF, Marty's parents met in a different way, and went on to be far more successful than they did before the past was changed. Even with all of these changes, all three of their children were still born. We could expect a similar outcome with Marty's and Jennifer's children.
Unclear, but unlikely.
The drag race (and its negative repercussions) are something that wouldn't have an immediate impact on Marty's relationship with Jennifer. Apparently even in the "crapsack" timeline she still lives with him and has his kids. There's no good reason to assume that in the "good" timeline this wouldn't also be the case.
The BTTF FAQ offers the following advice about timelines. Unless you do something really drastic, changing time isn't all that easy. Small events are simply glossed over in the "river of time"
There's a theory (we like to call it the "Self-Preservation Instinct of the Space-Time Continuum Theory") that says that the continuum is always trying to keep itself "on course," and when things happen to change it, it always tries to correct itself. It is much like a river, which tries to keep its overall course. Although earthquakes, fallen trees, floods, or other circumstances might disrupt it at points, the river would cut a new channel so that it would end up back at the same place. Thus, the overall physics (or metaphysics) of the space-time continuum would insure that any of Doc's memories of events that might create paradoxes would become hazy — or be erased.
I think it's fair to say that since the movie didn't state that he did, he didn't. We can speculate forever about what changes might have occurred with the changed future, but judging by the general lessons and tone of the movie, we can assume that life is better for Marty and his family without having raced.