Yes they can, and will eat bees and wasps.
However, they are not a daily food, and care needs to be taken.
While some forum members who hosue their chams outside year round or take them out for natural sun (which is a relaly really good thing btw) and their chams do eat the bees (stinger and all) most dont recommend it.
Now, if you want to feed the cham a bee, catch it, stick it in the freezer for a few minutes, just long enough to stun it still, then using tweezers, remove the stinger, then place it in the cage and watch.
yes they can swim, but dont try it at home.

And they dont need to clean themselves like a dog or cat does. they shed once a month until a juvi, then it starts to slow down. they dont really get that dirty, so to speak.
As a new member, I'd like you to fill out this form
https://www.chameleonforums.com/how-ask-help-66/
So that we can see how you are housing your cham, what you supplement with, feed it, etc. this way, if there are any issues that need to be addressed, we can do that before you come back on here with a thread titled 'my son's chameleon is dying, help!' which we see too often.
Welcome to the forums, good luck, and beware, they are addicting, as much for you as for your son!