Hello! I am new to Bonsai, and i just bought this juniper! It came with this pot, and i know i have to re pot it because of the sticking-out baby roots. After that, i'll wait a month to fertilize it with 10:10:10 solution because of the summer coming. It is about 3 years old, do you guys recommend wiring and pruning in some months?
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Look - in addition to all the other great advice given here so far, it's helpful to understand how a tree works. Let's break it down into three components: Roots, Trunk/Branches, & Foliage.
The trunk and branches merely provide structure and a conduit to bring water and nutrients up from the roots to the foliage, and food/energy generated by the foliage back down to the roots. You will, therefore need a balance between the foliage and the roots, since they are mutually dependent. If you have healthy roots you will almost always have healthy foliage, but not always vice versa, and you can't easily see the health of the roots like you can the foliage.
Even more so than with established bonsai, the emphasis for your tree is on its confined root system, especially with summer coming on. If I understand correctly, you don't really know the status of its roots - whether it was simply cut off of a tree in the ground somewhere recently and stuck in a pot to look like a bonsai, or whether it was actually established in its current pot for a matter weeks or months or years. Juniper procumbens "nana" are often sold in the former condition, and look great when sold and for a number of weeks or months after that - long enough for you to later think it was viable when you bought it and that you killed it, rather than realizing that it never had chance anyway and will invariably die no mater what you do. The small roots at the surface argue against that, but you still don't know it's history for sure. And since you don't know, perhaps, and summer is coming on, you can entirely ignore the trunk and the foliage for now: they either look healthy now for one or the other reasons just stated, or it doesn't matter anyway because the roots are nonexistent or terminally inadequate.
Knowing that, even if your tree is in good shape, I always like to focus on the weakened/compromised root system of a tree confined to a pot. This means you want well-draining soil, supplemented with things that encourage root healing, growth and function. You don't need nitrogen at this point: focus on phosphorous and potassium. I found, though your climate may dictate something different, that Kelp emulsion fertilizer fortified with a bit of humic and fulvic acid work best to keep the roots very happy, and growing and functioning well. If you stimulate the foliage to grow with nitrogen before the roots are functioning well enough to send them water and the building blocks for new growth you will stress the tree's balance, and it is more likely to die. If you're into the whole overly abundant/exuberant foliage styles, then go to town with your nitrogen, but even then you will need abundant/exuberant roots to support them, so fertilizers, supplements and soil types that support robust root health are key. They are not called "roots" for nothing. They are the foundation for the whole tree. I hope that helps.