Weld sizes normally include reinforcement height. Surface finishes shown on weld symbol using a line below the symbol. Uncertain as to the remaining issues of your question, but if the fabrication drawing is shows no finish call out, recommend not removing the reinforcement, it's likely intended to be left as welded. Lastly, a gambler is always a loser sooner or later, but a prepared mind favors chance. Don't bet until you know you've already won and quickly nobody will even think about betting against the Inspector.