12-18 inches year around is this a green color, check with secchi disc? If so no need to fertilize in fact it makes me nervous you are getting too many nutrients already.
No lime will not clear the pond, in fact it helps phosphorus make it less clear with more phytoplankton production.
Yes feeding lots of GG will put more nutrients in the water.
I'm not there put I would trust the local pond mgmr for his advice. Yep, too many cooks in the kitchen is a bad thing.