Can I save the map I make and use it in multiplayer?

Yes, but it will be zombies only. So, you need Wi-Fi to play with friends. And you need the season pass if you want more stuff.

Every single-player crafting recipe works in multiplayer, unless the server has plugins or mods to limit what items can be crafted.

It is calculated by Town Hall level and their actual loot. The lower loot count and Town Hall level, the lower the actual loot.

In order to play Minecraft online, you'll need an Xbox Live Gold account. You can play local splitscreen without any Xbox Live accounts.

Yes you can, because your AoE2HD is connected to your Steam Account. However, you can't play with strangers online.

You can't save over auto saves. You have to create a separate manual.