It means that your professor's suggestions are being considered and used. No, your sentences are not right. You must conjugate the verb correctly. I'm betting Vance corrected it in his head without even realizing it. If suggestions is plural, you must use have. My professor's suggestions have come into play. My professor's suggestion has come into play.

It means that something starts to have 'a use' . So in your sentence it means that you can USE your professor's suggestion (for something). And yes your sentence is correct.