Why do increase in firms profit margins cause cost push inflation? I read somewhere that this was the case. I get what profit margins and cost-push inflation are, but don't see how increase in marginal profit causes cost-push inflation? Also, how does increase in money supply cause cost-push inflation?
You can think on prices like $p = (1+m)w$, which means that prices are the value of inputs ($w$) multiplied by the margin ($1+m$) of the firms. So it is clear that raising firms margin would increase prices. This is cost-push inflation because the margin are part of the firm´s costs, it is a payment to a factor, like capital or entrepreneurship. 

A raise in money supply don´t cause cost-push inflation directly, but causes demand-push inflation, which can increase also increase the prices of productive factors and inputs to production (w) as well, if firms can pass this increases in their cost to produce to their price, then you have a channel of cost-push inflation.