Yep you can swim with them, you can do pretty much any thing except have intercourse
I bought one for my sister when she was working as a tour guide, going out to Fraser and Moreton Island for days at a time, she loved me for it!!
If I'm out and need to empty I just wipe mine out with toilet paper or wipes (I got some special wipes with mine when I bought it) , but to be honest I have probably only doen this once or twice as don't have a heavy flowm and if I planned to go out somewhere for the day or night - I would usually do a quick loo run at home before I left.
I have a Lunette and bought it from the Australian Lunette website (they have a great 'folding techniques' vid on there too.