First rule at my house: Food and toys MUST be supervised AT ALL TIMES. No begging. No random treating. Food is only available during training sessions and meal times. Meals are eaten in the crate. Dogs must stay in crate until I release them with an "Okay!". Dogs are released one by one into the yard for potty breaks. Dogs must wait outside until I let them back in. Even when I open the door for them to come back in, they MUST wait outside until I say "Okay!", at which point they can come back inside.

If you set similar rules about meal time (i.e. crating and vigilant supervision), you can avoid these food scuffles. Almost every multi-dog household I know has had scuffles like this, especially me. Their owners usually wise up and put into place stricter feeding time rules

Regarding the play time scuffle, it's really a matter of supervision and human intervention. Whenever your dog is interacting with other dogs, you MUST pay full attention. You should also have a decent knowledge of dog body language. If you don't, be sure to pay attention to the hardness of the eyes, the rigidity of the muscles, whether the weight is being held in the front or back, whether the dogs' arousal levels are getting frenetic, etc. As soon as you see something "iffy", step in and separate the dogs. Work on eye contact and calming behaviors. Then allow the dogs to play again. If you can't separate the puppies or if your dog is just too amped up to calm down, you intervened too late and you should start teaching your dog calming/focus behaviors, like extended down/stays, eye contact, touching his chin to your palm, etc.

Lastly, it sounds like your puppy has "claimed" your mom. This is not the type of behavior you want to see in a young puppy. Your mom needs to step up and assume her rightful position as leader. One of the most effective ways to do this is through NILIF, Nothing in Life is Free:
www.k9deb.com/nilif.htm
From now on, what the puppy wants, the puppy needs to earn - and your mom should make him earn it. If puppy wants to sit on the couch, your mom needs to ask him to sit or down or give paw. If your puppy wants attention, your mom needs to ask him to lay down first, etc.

Also, to prevent what sounds like the beginnings of jealousy, try cooperative feeding and petting. Whenever Loki wants petting, bring Jade over, put Loki in a down, pet Jade, and then pet Loki. Same for feeding. If you want to give Loki a treat, call Jade over, give her a treat, and immediately treat Loki. This way, he learns that Jade receiving good things means he will receive them, too. Jade becomes an ally, not an enemy. Good luck!