Per the pee leaks or wetness or accidents:
He is only 6 years old.
Per my ALL of my daughter's Teachers, from Preschool to Kindergarten to 1st Grade... they ALL unanimously said, that kids these ages have accidents. It is not unusual. Thus, in these grades, the Teachers request that the child has extra clothing in their cubby. And at my kids' school, even the Health room, has clean extra clothing/undies/shorts/t-shirts for the kids if they have accidents.
If a child has an accident or is wet, the Teacher does NOT make a big deal of it. This happens. They are young and not rocket scientists about it. Even my daughter, in Kindergarten and 1st grade, had some accidents.
My son, who just completed Kindergarten... some of his classmates had accidents at school or was wet. The Teacher never made it a big deal.
And the kids don't tease about it... because it is something that happens and the Teacher teaches them, that they are ALL children.
Now, as for night time... night time dryness is not something that occurs until even 7 years old, sometimes later. And kids these ages still wear night time diapers. It is normal and not unusual. It is about the physiological maturing and development of the organs. And it is NOT the same thing, as daytime pottying. Night time dryness, is a completely DIFFERENT timeline and development.
Just use a water proof bed pad under him, and so the sheets do not get soiled. Me: I have like 4 of them that I use under my son (who is 5) and I rotate them. The sheets do not get soiled. I got the waterproof bed pads from Amazon. They have many.
ALL KIDS... have daytime and night time accidents.
It is childhood.
It is normal.
And many young kids, do things like chew on their shirt, or twiddle their hair, or chew on their nails. It is a comforting thing, and can be when they are stressed or even just bored.
They grow out of it.
When he is about 2nd or 3rd grade... kids those ages change. And you will not see the frequency of these "young" child things.
There is something called "Potty Scotty" underwear. It is a padded underwear. Typically used for potty training. However, my son who is 5... wears these. He can still fit their XXL size, which is for up to 49 pounds. My son is a bit more than 49 pounds, but he is lanky and can still fit his Potty Scotty underwear. Anyway, the reason still he wears it is because he still fits it, and it is padded... so even if he has a bit of pee wetness, the underwear contains it, and it will not drip down his leg. My son actually likes these underwear, because again, if he leaks or has a slight pee wetness, it will not drip down his leg. The underwear absorbs it well and it is not embarrassing.
Here is the link for it:
http://www.pottyscotty.com/Kit-0018.html
http://www.pottyscotty.com/CTGY/Potty-Training-Pants.html