Soldered splices and wing nuts are against boat wiring codes. Crimp or splice type connectors are the preferred method. Dielectric grease will prevent corrosion. Heat shrink tubing can be used over the dielectric grease. However without the grease, shrink tubing will trap the moisture and it will still corrode.
Best to use the same diameter wire for the entire run. Fuse accordingly. Fuse protects the wire not the device. Since this is a motor, you want a fuse rated for motor use. Motors draw significantly more power at start up and once up to speed drop to normal loads. Too simplify things, most trolling motor companies have a rated sized fuse for the model of trolling motor, ensure your wire is large enough to meet that rating. Wire size also depends on length of run. Length of run is from the battery to the device and back to the battery. Both directions. I highly recommend a resettable fuse.
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