Is it intended that there are no fees at all? When I try sending, it doesn't charge me. And there isn't a field to specify what the fee is.
Yes
In the spirit of seeing what LTC would be like when the block reward hits zero, I sent a transaction with a fee. I then mined that block and got the fee back.

I really think that for any coin that sees widespread use, the transaction fees could easily support the coin when the block reward hits zero.
Good find.