Sentence 1: Either way works. No difference in meaning. An airplane can literally "go" or "fall"_ downward_.
Sentence 2: Either way works. In this case, the economy went or fell downward figuratively (to a worse condition).
Note that in both 1 and 2, the subjects (airplane or economy) are inanimate, so there is no question of intent or volition.
Sentence 3: Either works, but "fell" could be seen as attributing the depression to outside forces, whereas "went" would not, because it implies the person is assumed to have some choice in the matter (less or more, depending on whether the speaker sees depression as a disease or as a failure to try to keep a positive attitude.))
Sentence 4: "Fell", as in #3, implies that the habits happened to him, not by his desire, but perhaps because of inaction, or of being in a bad place (among friends who used drugs, for example). This minimizes his blame in the matter. It wasn't really his fault; he just "fell". We might even say he fell in with a bad crowd, and [consequently] picked up some bad habits (like falling on the ground, and "picking up" dirt on one's pants.) Thus he is exonerated, in the eyes of the speaker. (If it's his mom speaking, that's what she'll claim at his trial.)
But if he "went into some bad habits", that would imply that he intentionally sought them out. And we wouldn't say it that way!
We might say he acquired some bad habits, or he got into some bad habits. These are not exculpatory, as the above, but both are neutral—that is, non-judgemental.
But, If we wanted to put blame on him, we might say, for instance "He has taken up smoking. (or, more antiquatedly, "He has taken to smoking") That is, the speaker thinks that he could have refrained, but that he chose to "take" the habit.
So you see that "went" vs. "fell" doesn't matter with regard to things, but it can matter, in subtle ways, in regard to people.