Yes, if a verb is transitive then it most often connects with Accusative without any preposition (some verbs connect with Genitive). English follows SVO word order so if there is a noun/pronoun before and after a verb in English sentence then you can assume that the verb is transitive and the direct object of the verb will appear in Accusative. In Polish the subject of the sentence is implied in the verb form.
"przypadek" is when something happens accidentally, by chance, also "coincidence". Other usages include "w tym przypadku" (in this case).
"wypadek" is mostly something like a car crash. But there are other usages, like in "na wszelki wypadek" = "just in case".
Very strange that those can be the same word in English...
It's not strange if you look at it in the right way. An accident is something that happens to you which you didn't cause, or didn't intend to cause. A coincidence is something that has no cause at all. The boundary between coincidence and accident is just at a different place in English from where the boundary between przypadek and wypadek in Polish. For me it is very strange to say "w tym przypadku" for "in this case" as there is nothing at all to link it to accidents and coincidences. It just shows that all languages are strange!