All alternator regulators have diodes that prevent the flow of current from a battery to the alternator.
I don't see a problem running both motors at the same time connected to the one battery. Each battery will contribute a bit of current to the battery.
But as the man suggests, if there is...
I don't know personally that your motor uses a decompression mechanism. My comments were based on you saying that it has one.
Have you thought about the possibility of a lower unit problem causing the motor to be difficult to pull start?
Easy enough to remove the lower unit and then use the...
There normally no over compression. It is just that normal compression makes a four stroke motor hard to pull start. A decompression mechanism momentarily prevents full compression when a starter rope is pulled.
Mercury Marine has approved a number of models for use with lithium batteries.
Although not approved by Yamaha, Suzuki, Honda or Evinrude, a number of owners of those brands are using lithium batteries with no ill effects.
CDI unit gets its input from the charge coil. It "charges" a capacitor within the CDI unit. The pulser coil tells the CDI unit when to discharge electrical power to the ignition coil.
www.yamahapubs.com