Just be careful about where you make your dock and park your ships. They won't move if nobody is on them and stay put as soon as you exit the boat (this is a great strategy for hard-stopping your boat if you think you're about to hit something nasty or need to stop in a hurry, just jump out).

However... While the boat itself may not move, during storms the sea WILL. It will rise and fall quite dramatically in bad storms. You need to pay very close attention to what the shore is like and anchor your boat so that it is not in the water above any rocks or sunken logs or too close to shore. As the sea rises and falls your ship will smash into those rocks beneath it or ground itself out on the shore. This can (WILL) destroy your ship.

If you're close enough to shore it isn't a big deal as you can wade or swim out and gather up the materials and just remake the vessel. If the ship was too far out, you will only be able to collect what ever cargo was on the ship and the wood (wood floats).

Many a time have I thought I had parked my Karve in a good spot only to return and find that it has broken up on a rock I had parked it above after a hard storm. Not a great time.

As for the cart, they can be super useful at all points in the game. Slow and tedious at times, but much better than making ten trips back and forth any great distance. I've got the darn things all over the place. They do deteriorate due to weather (down to 50%) and can become damaged during use. To keep them at top condition I build little cart-houses for them; just a frame structure with a roof over it to keep them out of the weather.