A Solar Charge Controller regulates the voltage and current flow from solar panels to a battery. It detects and monitors the battery voltage, reducing the current when the battery is fully charge. The controller maintains a float charge to keep the battery ready for use.
A solar panel can run a trolling motor depending on the solar panel size and the motor power. However, it’s normal to run a trolling motor from a battery and a solar panel.
Monocrystalline solar panels are the best all-round choice for efficiency, cost and length of working life. Polycrystalline panels are less efficient but also less expensive. In this case, choice can depend on your budget.
Such a solar panel connected to a battery in bright sunlight will charge the battery and keep on charging it over and above normal recommended voltages. It would definitely damage the battery internally. It’s important to use a suitable solar charger.