Well, following the guidelines of your foodbrand is usually not the way to go. For some dogs the given amount is too much and they grow fat, for some dogs it just isn't enough. i feed by eye, meaning my dog should look lean. When you put your hands on the sides of your dog, about a hand witdh behind the front legs(pointy bit, elbows) you should be able to feel the ribs of your dog, without putting to much pressure on your fingers. Because your dog is still a puppy you can allow some puppyfat.
But I would NEVER give the dog unlimmited acces to food, especcially when there is a lab in the mix. Labs tend to overeat. Heavy dogs( fat dogs) are not happy dogs!
When you are training you can use light treats, like boiled chicken(my dogs love that)or look for diet hotdogs(less fat)
The picking stuff up, that is pretty normal, I think, for a puppy. It doesn't have to be because he is hungry. They want to investigate things and it is up to you to teach him what he can pick up and what not. So I would teach him " leave it"
If this is happening around the house, he picks up or chews on maybe a slipper or what ever, just trade him for it with something he is allowed to chew on(like a bone or a toy). You hold the bone or toy in front of him, and as soon as he drops the item in his mouth, you give the bone. You can add a command to the dropping part. Leave it, or drop it. Say this the moment lets go.