Investing in/on?
"It is widely argued that investing money on roads and freeways is more imperative than on public transportation."Why in this sentence used "on" instead of "in" and why invest is gerund?

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I agree with Karen.  I think sometimes the sentence is similar to another sentence;
I would say 'investing in roads' but 'spending money on roads' so I thnk the writer confused these two ideas.
It's a gerund because it's something - THIS ACTION (investing in roads) is...

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It's not really correct.  The writer is using 'investing' as if it was 'spending', (which is really what they mean) when 'on' would be the correct preposition.  Investing should be followed by 'in'.