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What Joe said and then some. The way the alternator/regulator should work is it puts out around 14 volts regardless of RPM (the regulator regulates the voltage). There may be an exception at idle. Many alternators need a minimum RPM to function and at our engine idle speed of 600 RPM and the typical 1.75:1 pulley ratio, it's not enough. As soon as you rev up a little it works fine.
Your reported voltages are a fright. At a minimum you need a new regulator. I recommend removing the alternator (and regulator if not integral) and taking them to a proper marine alternator shop for bench testing. Following that compare the cost of repairs to outright replacement. The low voltage you're reading at idle on the dead battery is because at that low RPM the alternator can't deliver all the amperage the battery needs so it's sucking the voltage down. The high voltage you report is completely out of line and as Joe said, will cause damage to everything connected to the electrical system.
Your reported voltages are a fright. At a minimum you need a new regulator. I recommend removing the alternator (and regulator if not integral) and taking them to a proper marine alternator shop for bench testing. Following that compare the cost of repairs to outright replacement. The low voltage you're reading at idle on the dead battery is because at that low RPM the alternator can't deliver all the amperage the battery needs so it's sucking the voltage down. The high voltage you report is completely out of line and as Joe said, will cause damage to everything connected to the electrical system.
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