"Over" can have two relatively distinct senses: the most basic is "above" (not touching), and the more specific is "across", probably as an extension of the former ("walk over the river" > "cross the river via a bridge" > "walk over the bridge"). There is also another sense where touch is involved, as in "you can run your hand over this fabric to feel its texture", but that seems to also be an extension of the other two.
The reason that your #2 is bad is because there are other prepositions more likely to be used in that scenario, so in contrast "over" isn't a good fit. This is probably an example of blocking (e.g. we have "thief" so "stealer" sounds wrong), rather than "over" not being allowed there. But notice also that your #1 is actually ambiguous (walking across the bridge vs. walking above the bridge-- on another bridge?), so that is important for addressing the other two.
It would be better to give a paraphrase of what sentences #1-3 are supposed to mean if you want more specific feedback.
