Can an owl be tamed and deliver letters? If so, how could it be trained and what would be its responsiveness towards us? Also, is it legal or is it too dangerous due to its talons?
Short answer: NO
Delivering anything to a remote place is an extremely difficult task for any animal.
I could find evidence of messenger dogs and the occasional horse used in several wars to autonomously deliver messages and provisions to and from the front lines. What they actually did was return to a trainer they were very closely bonded with. One soldier had to take the animal to the front line and keep them there, then attach a message and send them off to their bonded trainer. Some dogs could be bonded to two trainers, running errands between them:
A liaison dog, which took about twice as long to train, recognized two handlers, and could be directed by either to return to the other. These dogs could be sent back and forth continually between the front to battalion headquarters. Although Richardson trained some liaison dogs, he noted that this “more difficult system” entailed “a considerably greater wastage of life, both among the men themselves and the dogs, as the position of the keeper in the front line is fraught with risk, and the dogs are also required to run a double journey over the danger area.” (source)
Carrier pigeons have been used by humans for hundreds of years, but they don't deliver anything either. All they do is return home to their loft, finding their way by visual, auditory and olfactory clues and even navigating the Earth's magnetic field. You have to take a pigeon away from home, attach a letter to it and let it return home, hoping that someone will retrieve the letter from its loft.
In contrast to dogs and pigeons, owls are undomesticated animals. You have to get an owl used to humans from a very young age to even be able to handle one without it flying away. There are reports of owls attacking humans and pets.
Owls can be trained to fly to a falconer / trainer and land on their arm. This only works because the trainer offers food every time the owl lands on their arm. The owl has no other reason to fly to the trainer. Without food, no owl. They don't get attached to humans, they just learn that landing on a specific human yields an easy meal.
Additionally, owls do not have a loft or nest they reliably return to. Take an owl too far away from its home and it will simply find a new home.
Popular movies and TV shows depict owls and ravens delivering messages, and there have been attempts to use cats for mail services. But all these are either spectacular failures or no more than imagination. Despite ravens' widely recognized intelligence, humans have not managed to make ravens deliver anything to anyone.
It seems that to deliver messages, an animal needs to be very tightly bonded to the person or place they're supposed to deliver to.