So for those who are studying from the app I take it that all these prepositions like vor mit bei and nach have to be followed by dative?
Correct, a more complete list would be: aus, außer, bei, gegenüber, mit, nach, seit, von, zu. There are others of course, but those are the main ones.
Then there are two-way prepositions that either take the accusative or dative: an, auf, hinter, in, neben, über, unter, vor, zwischen.
Explaining when to use accusative and when dative is far too complicated for a short comment like this, but the basic rule is DRAM - dative rest accusative motion. So if the sentence is expressing a position (rest), it's dative, if it's expressing movement (motion), it's accusative. There are more complex rules and some idiomatic expressions don't seem to follow any rules but this is at least a start.
And then there are, of course, the handful genitive prepositions:
Well if we're going to mention genitive prepositions, maybe I should also add in the accusative-only prepositions just in case: für, um, durch, gegen, entlang(*), bis, ohne, wider. I learned these with the mnemonic "fudgebow"
Just note however that entlang IS technically a two-way preposition, but it triggers the dative case so rarely, a lot of textbooks just include it with the accusative prepositions.