When we 1st moved aboard we kept them in for a couple of weeks to settle in but now they are allowed off the boat when we are on a safe mooring ie out in the country away from busy roads ect. They come back to the boat no problem as they regard the boat as home just as when we lived in a house.
If we are moving on I don't feed them until they are safely back on board ;-) Hasn't happened yet but if they go walkabout we will just have to delay departure till they return, good job we are not in a hurry.
I keep the doors closed when we are cruising as don't want them jumping ashore before we are ready! I deal with the litter same as when we were in a house - bag and bin it.
Also, not too sure about Charlie yet but both Poppy & Soona have fallen in & can swim quite well ( not that they liked it much!) If you check my blog's older posts back to 2008 you can read more.
Good luck with it all & when you come over say hello :-)
