One challenge could be controlling the extent of his power. For example, he might accidentally cause a huge overgrowth of plants that start to overrun the Hogwarts grounds. It's difficult for him to fine - tune his ability at first.
He might face opposition from other wizards who are jealous or fearful of his power. They could try to limit his use of it or even plot against him. Also, in the magical world, there are rules and regulations, and his new power might not fit neatly into the existing framework, so he has to deal with the Ministry of Magic's potential interference.
The magical creatures in nature might not always be receptive to his control. Some might be very independent - minded and resist his attempts to influence them. For instance, a group of centaurs in the forest might see his power as an intrusion on their territory and their way of life, and he has to figure out how to coexist with them while still being able to use his power when necessary.
One challenge could be controlling the intensity. Lightning is a very powerful force, and it might be difficult for Harry to rein it in. He could accidentally cause too much destruction when he just wants to create a small spark.
Perhaps it's through an accidental encounter with a powerful magical plant. He tries to interact with it in a normal way but ends up influencing its growth and behavior. This unexpected event makes him aware of his unique power to control nature. For example, he might touch a withering plant and suddenly it springs back to life and starts to grow rapidly under his touch.
One challenge could be controlling the intensity. Lightning is extremely powerful, and if he doesn't have proper control, he might end up causing more harm than good. Another might be the unpredictability of the element itself. Lightning doesn't always behave as expected in nature, and it could be even more difficult to manage magically. Also, he may face opposition from those who fear his power or think he's becoming too powerful.
One challenge could be the basilisk's own will. Even if Harry has the ability to control it, the basilisk is a powerful and ancient creature with its own instincts. It might resist Harry's control from time to time, especially when it comes to situations that go against its natural behavior, like being made to not attack innocent students.
He might face political intrigue. There are likely those in the Wizengamot who oppose him due to his past actions and his association with Dumbledore. Also, he has to deal with the complex and often archaic laws and traditions of the wizarding world which could be a huge obstacle.
One challenge could be controlling the assassin's violent tendencies. Since the person is being groomed to be an assassin, it's likely they have a natural inclination towards violence, and Harry has to find a way to temper that while also teaching self - defense.
Well, in such a fanfiction, he might control space through his magic wand. Maybe he uses a special spell that he discovers or invents, which allows him to manipulate the fabric of space, like creating portals or warping distances.
He also has to deal with the secrecy around wand - making. Since it's a highly guarded art in the wizarding world, he might face opposition from the Ministry of Magic or other wizards who think he's meddling in something he shouldn't. Plus, he has to make sure that the wand he crafts is unique to him and suits his style of magic, which is no easy feat.
One challenge could be dealing with the traditionalist teachers and pure - blood families. They might resist any changes Harry tries to make as they are used to the old ways. For example, if Harry wants to introduce muggle - born friendly policies, some of the old - school pure - bloods might oppose it.
One challenge would be the goblins. They are very protective of Gringotts and would not easily give up control. They have their own laws and traditions regarding ownership. Harry would have to deal with their resistance and find a way to convince them or negotiate with them.