Initially 10. Later on you unlock it to 15 permanently, and a special proposal in a assembly allows you temporarily raise it to 20 for a single battle, which this proposal can be passed as many times as you like.
Treasure Boxes on maps are not automatically acquired at the end of battle. You must destroy them to get the items inside. Eventually the Thief class gets a skill called Thief Key which allows you destroy any treasure box in a single blow.
The classic sprites don't exist for D5 because some characters literally don't have them. mainly some of the DLC characters such as Metallia, the new classes like Maid, Wrestler, Dark Knight, and so on, including the new main cast.
Actually yes, multiple benefits. Casting spells or using skills level up based on how many times you use them. So you can get free skill exp just for wasting these inanimate objects. Same applies for weapon exp. Also much later on in the game you can create your own custom battle maps, Each object you destroy is unlocked to be used as a placeable object when creating your own maps. So try and destroy everything you see.
In the Netherworld Base, there is a Moth NPC called the Data Shop, talk to him, buried in his menus somewhere is a BGM option that allows you change the music to the base and several other locations. You can change the music to whatever you want the only restriction mind you you had to hear the song at least once in-game previously.