Potassium thiocyanate and iron(II) acetate
As best I can tell, your answer is correct. I can't find any reference for iron(II) thiocyanate in the form your teacher says is correct, and several references that say $\ce{Fe(SCN)2}$ is the correct form.

For precipitation reactions, the charge will never change. You should always assume that the charges in the product will balance. There might be some cases where the product has an unexpected formula that you can't predict based on charges alone, but I can't think of any off the top of my head, and you certainly shouldn't be expected to know them at this stage.

edit:

This is the best reference I could find, it's a google books link to the CRC handbook