Good question. Any online references to it seem to be English-German or German-English translations. My girlfriend, who's German, says it's commonly used, though. Be interesting to know if its usage has been picked up from the English phrase.
Why is this "ihn", not "ihm"? Someone please correct me if I'm wrong but I thought that auf as a 2-way preposition is accompanied by dative when there is no movement?
the movement is a little metaphorical here. perhaps an easier way of thinking about auf (and other 2-way prepositions) is that its accompanied by accusative when it is not being used to locate something, i.e. "Das Buch ist auf dem Tisch'
Ah thank you! That makes a lot of sense, I had been approaching 2-way prepositions in the opposite way to your description (ie. using dative unless there is a definite movement, rather than using accusative as long as there isn't a location). Thanks for correcting my approach, much appreciated :)
I didn't think "depend" would work, but I took a shot. It has the same meaning in American English.
on it should also be accepted here since we don't have any further context. The ihn pronoun may refer to anything grammatically masculine, it doesn't have to represent a person. I’m not sure why someone downvoted your question
In English, it's a common expression: "You can count on me," "Can we count on your support?" etc.
But why is it only 'I would' here - 'I will' is not allowed?
Yes, Abuscato's right. Offhand, "would" is, most simply, part of conditional, like "I wouldn't count on him IF I were you." At the very least, it's a hypothetical, and works like a suggestion. In English, and having studied German in the past, I'm gathering it's pretty similar.