I think all of us have experienced the following at some point. You're showing off your new puppy/dog to your friends, perhaps trying to get him to do some tricks, but new puppy/dog has other ideas and starts to try and bump and grind anyone and anything in sight.
Although we consider our pets to be family members, always remember that dogs do not think like us!If you observe puppies in a litter, it is not uncommon to see the males attempt to mount their litter mates whenever possible. Female puppies can also exhibit this behaviour, although it is not as common. All dogs are pack animals, and the puppy is simply trying to determine his place within his family pack and this transfers to his new 'family'.
Dogs do not comprehend how a present action will affect future events, they can however, use past experience and will realize that puppy humping felt good in the past, and will make them feel good now. He cannot understand that humping another dog or item today will affect his social standing in the future. This is completely beyond his understanding.
If your puppy is in an excited state or state of arousal and is performing objectionable acts, the solution remains the same, he needs to be calmed down by using "Sit" or "Stay" commands. If your dog doesn't respond to this, place him in his crate until his excited state passes. Your dog should learn quickly that puppy humping will result in an automatic crating, which should curtail this behaviour. Remember the crate is not to be used as a form of punishment or imprisonment, but a place where your puppy/dog feels calm and safe
In the end, almost all dogs will exhibit signs of puppy humping at some point. Although embarrassing, it is not really a problem so long as your dog is not hurting anyone.
The general consensus is that if the puppy humping is not harming anyone, do nothing. Given enough time, it will resolve itself on its own when your puppy understands his social standing in your family. Do not allow the puppy to become the dominant member of the family! You and other family members will have to demonstrate your dominant position by using "Sit" and "Stay" commands whenever your puppy starts to mount someone. Do this for 2 months and it is still an issue, you may want to consult a professional animal behaviourist, who may organise a comprehensive behaviour management program or recommend having your dog neutered.
With regard to castration, there is now a believe that males should not be castrated until they have been cocking their leg for at least one month, and should be at least 10 to 27 months of age (depending on size and breed). The larger the breed then the later they mature,. therefore something like a German Shepherd would be much later, probably more like 17 months. Unless of course there are medical or serious behavioural issues to take into consideration.
In females, the believe is that they should have at least one season, preferably two, then wait approximately 3 months after the season before considering spaying, allowing the internal organs to settle down after the season.