Is that protection or jealousy?

Mango is only 5 mths old but I see a change in her behavior. When we go for walks and a dog comes towards us, she will run and stop right in the approaching dog and stops the dog from coming towards me. If I start to go and pet the other dog she will jump and push my hand away and snap at the other dog. Also if my bf plays a little too rough at me, she will look up and stare at him like "what the hell are u doing to her" And I will have to say I'm alright before she lays down again.
She is so alert nowadays to pple walking pass our door and she will go investigate to see if my door is closed and comes back to see if i'm safe, goes back to the door, listens that the pple have gone before lying at my feet again.
Is that normal for a 5 mths old puppy to behave?

Get a handle on this as soon as possible. This is not a desired behavior for any dog and could lead you to getting in trouble down the road. Get yourself and your pup to an animal behaviorist or a good obedience trainer who practices positive training only. You need to teach your pup that this is unacceptable behavior.

It's not normal for a 5-month-old pup to be that protective. Most known guardian breeds, like mastiffs, don't usually become protective until maturity. I agree with Athebeau. Look for a trainer now. If the problem is not corrected, she will only become more and more protective as she gets older.

My little pup does the same thing.. almost! She'll grow if someone comes to the door or if were in the front and she see's someone walking/running by then she'll grow at them and want to chase after them. Like you, I cant tell if thats her being protective or if she'll grow out of it. She's friendly to other dogs though.

The problem also lies with the owner in a lot of cases. Many owers inadvertely encourage this behavior. For example the puppy growls the owner says softly "there there Brutus be nice", the soft voice reinforces the the growling. Some owners think its' funny or cute to have an over protective pup. A friend of mine had a Shepherd pup and it started showing signs of being possessive at a young age. My friend, (even after I told her not to encourage this behavior) ended up in hot water later on when her Shepherd attacked a child that got to close to her child. No warning, her little girl had always had little friends over and the Shepherd showed a little bit of pushiness with my friends child, sometimes getting between her and her friends. The owner/childs mother and father thought is was really cute and that the dog would protect their child in case of an emergency. What happened was the dog was timid of big men and did not show any protection of the child with people who may hurt her, but, the dog did end up biting one of the childs little friends so badly the child ended up in the hospital with facial disfiguration which she ended up having to get plastic surgery. My friend the owner of the Shepherd got sued and the dog had to be destroyed. It was an unhappy situation all around, and it could have easiely been discouraged at a young age.
Just keep in mind; this behavior is not cute, and don't encourage it in advertely (soft talk, petting the dog while it's being protective) these actions encourage the behavior.
That is basically encouraging her. In some peoples minds they think "hey, my dog really loves me". When in fact they are resource guarding when they are doing this. Get a handle on this behavior. If your dog shows any sort of bad behavior when you are having fun, give the dog a time out or make the dog sit and then reward for the desired behavior.

Ours are, as most of you know, guardian/herding dogs and they DO exhibit this kind of attitude at an early age, and it's what they are SUPPOSED to do. It's our job to teach them what is important to pay attention to and what should be ignored. Mine simply got told to go back and lay down, that nothing was wrong. They learned to relax and not pay attention to normal situations that way, but will still alert when something out of the ordinary comes up. Now they are getting more adult and will simply raise their heads or sometimes get up to go investigate and relax as soon as they've ascertained that there isn't anything suspicious.

I have always used the term "it's ok".In Roxies' case that is her cue to chill and go lay down. There have been a few people she did not like, and probably didn't like my decision, but she has been trained to obey that command. I will raise Brutus the same way. The main thing is to know what your breed of dog has been bred to do. It is then your responsibility to train your dogs to respect you and know the difference between nothing to worry about, and the possiblity of danger.

I don't see this as an abnormal behavior at all. What breed is Mango? Many dogs show protectiveness very early. A Doberman, for instance, mine in particular, started showing protective behavior at around 4 months of age. I don't see a huge problem. More socializing and managing her reactiveness will go a long way. Your dog doesn't have to love every dog it meets. That is not natural for dogs to accept every dog into their group. You can teach her to associate other dogs (from a distance) with good things to optimize the situation. If there are some dogs she does know and like ....(like friends' dogs) arrange play dates.

When she comes face to face with strange dogs, they can be giving off body language that you don't notice which causes her reactiveness. I'd steer away from meeting dogs face to face and set her up to walk in the same direction as other dogs are walking. Get her more use to that first and give treats and praise when she is non reactive.

Again...it is not normal for dogs to accept every dog they meet or appreciate a strange dog in their or your space. It is entirely normal the way your dog is behaving.

She is a white GSD, she is friendly with other dogs, will play with them, she just dun like me to pet them or get close to them. But I do not encourage that behavior, if she starts to snap at the other dog, I'll tell her in a stern voice "No" .
Yea, i use its alright to get her to lay down too

Being stern when she does that will often backfire on you, as she will associate the dogs and your touching them with a bad time. "Oh no! Mom's touching a dog and that means trouble." Try desensatizing her to that. From an ample distance, have a friend hold her on a leash while you go pat the other dog. As long as she is remaining calm, she gets some super yummy treats and praise. Do this for a long time.....from a distance. Gradually decrease the distance. Put her in a down/stay (if it's pretty reliable) and have someone there to enforce that if she gets up. Show her what behavior you like and what gets her praise and treats.

At other times, I would impliment some of the NILIF because she needs to understand better that you are the one who calls the shots, not her....that you have it all under control and she doesn't need to take the law into her own hands so much. LOL. This will help temper things down, but may not completely eliminate that behavior when you're close to another dog. It would take some real consistant practice and counter-conditioning.