Is it permissible to hunt pigeons for amusement and recreation, and is it permissible to eat these pigeons that die after being shot in the air?

Hunting for amusement is reprehensible (makrooh tanzeehan), and it may become forbidden (haram) if it is solely for the purpose of killing without the intention of ritual slaughter (dhakah), as this falls under the category of corruption (fasad). However, consuming what has been hunted for amusement is permissible if the hunter intended ritual slaughter.