That might just mean more competition is created as there's a bigger market to chase. Minimum wage has the same risk as the one you mentioned, but also all but guarantees higher prices (particularly on labour-intensive goods such as food) as everyone's wage needs to go up to make the harder/worse jobs worth doing.
I'm not sure what you mean. Prices rising is what we call 'inflation' - one doesn't cause the other. They're the same thing.