Maybe not the English longbow, but some contemporary longbows elsewhere in Europe (such as 15th-century Burgundy) were clearly recurved.

many different comments - hard to pick out in order to reply - please look for the response to your own 'bit' .

Regarding volleys or single shot. a few points for consideration

Volleys were disruptive in nature. A hail of arrows could not be totally ignored even by those in armour - and they affected the horses as well. Loosed from the flanks they tended to force the oncoming army into a tighter bunch, making movement more difficult

An arrow following a high trajectory loses very little in power, it is effective throughout its full range, - largely due to the effect of gravity on its way down

If your enemy is advancing on foot through thick mud you can get quite a few aimed shots at individual men. If they are advancing rapidly on horseback you will be lucky to get 3 or 4 arrows away before they are on you.

Penetration is not vital to stop a man in his tracks. Blunt trauma is considerable and can kill - or at least take a man off his feet. Older less able men could find getting up impossible. Some did suffocate in the mud.