Hello,
I have recently bought a fairly cheap Ligustrum (as the label said). I am planning on buying another Bonsai shortly.
But honestly, I am very new to this and don't really know what I'm doing yet. So, I've got a few questions.

1) Is the pot big enough for the plant to grow steadily?
2) The leafs seem kind of dry. How often do I need to water the plant?
3) Is it possible to wire the branches? It feels like some branches are tough and would probably break when pushed too hard.
4) Should I worry about the roots growing above the soil?

Thanks in advance! Any other tips are welcome!

1, I would repot into a bigger pot. Then the roots will have space to grow.

2. You water the tree, when the soil is dry. The soil needs to dry between watering. But the soil may not dry completely out

3. Yes.

4. It is normal that roots grow above the soil. But I would repot into a bigger pot and let the roots and tree grow.

Good luck

This plant does not need a bigger pot. It may need to be repotted, Wiring the branches is problomatic as they may be quite brittle and very difficult to bend but then the branches are reasonably well placed and therefore there is no advantage to wiring. The shape or style is broom, and it would be difficult to change that without being very drastic whic as someone with no knowledge of styling might just be enough to kill this plant. You would be better to buy a book, read what is on this site before getting anything else. All plants belong outside and therefore I would suggest that you find a hardy species for the next plant you get and go somewhere and choose it do not buy blind on the internet.

First of all, bonsai is a marathon, not a sprint. Iow: you have time to do things.
Second, how green are your fingers? I would say not that green because of all your questions and the fact that your plant is inside the house, which will kill it sooner or later.
So, study some basic horticulture first, read up on bonsai second, try and keep your plant alive and go from there...

I do agree with Hansen, it will grow better in a larger pot. Broom style is difficult and it will take a lot of growing and training for it to become a full canopy broom.