downloading game data

No u cant. The game data comprises of all the servants' and CEs' art, dialogue, etc. You still need an internet connection to play the game

Downloading game data can help the game run better/faster but you always need an internet connection.

if you want to play the game while on airplane mode you can turn it on and then turn on the wifi, it worked for me on my android.

The download data just dumps all the info about any servant, voice, np, quest, etc that you haven't encountered yet so there is no lag when you encounter it. Playtime still requires the server to determine quest drops, record battle completion, summon results, etc.

No. FGO is quite friendly to slow or unstable connection since it does not check the server very often during combat, but you still need a connection for play.