First of all, are you actually WANTING this pair to breed?
Before breeding any species, it is important to learn as much about the animals, their personalities and the best practices to follow for responsible and ethical breeding prior to making the commitment to take on this responsibility. This requires extensive research and an openness to continual learning and members will want to ask you certain questions to assess whether or not they feel that you are well prepared, before giving advice to proceed with breeding plans.
With regards to your male bird’s behaviour - Male masturbation in itself, is relatively harmless. As long as there’s nothing sharp or pointy and he’s not doing it all the time, he probably won’t hurt himself. Unlike female budgies who can get egg-bound, in male budgies this behavior is relatively harmless.
Animals feel no shame in expressing their sexual urges. It’s normal, totally natural behavior and he’s doing it because he has an instinctive urge to and it feels good.
However, this hormonal behaviour can be accompanied by regurgitation. This can in some circumstances become excessive and lead to the male bird becoming undernourished.
If your bird is also excessively regurgitating, it’s usually recommended to remove the item if it’s a certain toy/perch/accessory that is the source of attraction. In this case, it appears that your bird is using multiple sites and so this isn’t really possible. I would however, remove the mirror which can often be a source of frustrating unrequited love. You can discourage the practice by distraction and redirection. Redirect your bird's attention towards toys and healthy interactive play with you, the owner. It may also help to scratch your budgie’s head (if your bird is happily accepting of you doing this) as this will often trigger them into the alternative activity of preening. Stroking and scratching around the head is fine, but scratching around the back, rump, and hind end may cause sexual stimulation.
Your bird should never be punished or disciplined for masturbation.
It great that you have joined the forum. Stay around and have a read through the stickies:
There is a wealth of information to be gained there.
*Oops! Seems that Therm was succinctly posting at the same time as I was composing this rambling essay