Harrison Ford has always been very private. He doesn't like discussing his personal life. That's one of the reasons he doesn't live in or near LA/Hollywod. He has a huge ranch out in the middle of nowhere.
They had Shia on SNL because he appeals more to the "target audience" for SNL. Generally speaking, it is a show for younger viewers.
As for him taking over the series, I think a LOT depends on how well this movie is received. It'll make a ton of dough the first couple weekends no matter what. But, it could easily tank after that if it isn't all that great.