Can a character really grab a arrow out of the air coming straight at her from afar?

It’s in the range of the possible, basically a yes and a no. You can do it in a controlled environment and it is one of those famous trick shooting stunts, but it requires both participants to be working together. The seconds often don’t get enough praise for their skills and their ability to safely support their partners. Much in the same way we don’t celebrate Hollywood stuntmen and women for how well they train actors and how good they make them look on screen. It’s a fantastic trick, and worthy of all respect to whoever can pull it off.

In a live combat situation, it’s a no. There are too many extenuating variables and it is actually far too chancy to even risk yourself trying it. I mean is the coolness factor of grabbing an arrow out of the air really worth getting shot over? Even if you can time it right, the friction will tear up the hand if it’s barehanded. This means your character sacrificed their hand for the rule f cool. There are too many uncontrollable factors at play in a real battle situation for it to even be considered. An arrow is neither a spear nor a javelin, you can play catch and release with one of those. The northern Germanic tribes are documented using this tactic against the Romans. A javelin or spear is substantially larger than an arrow and the reason why the Vikings could do it was that they practiced throwing sticks back and forth as children. It was part of a game. If anyone is wondering how one trains children for wartime, the answer is you turn many of the necessary skills into games, normalize them, and make them part of the culture.

In regards to trick shots, the character might do this to show off with friends and a trusted partner in their downtime.

For a character like a D&D monk or another character type with superpowers or heading toward an enlightened state/ascension, then it’s not that out there. You just have to be able to justify it in setting and there should be a little more at play than just “oh, really skilled people can do that”.