There is a 0.3% fee for swapping tokens. This fee is split by liquidity providers proportional to their contribution to liquidity reserves.
This fee however could be changed for each pair via a Governance Proposal, more information can be found in the Change Fees proposal information.
Swapping fees are immediately deposited into liquidity reserves. This increases the value of liquidity tokens, functioning as a payout to all liquidity providers proportional to their share of the pool. Fees are collected by burning liquidity tokens to remove a proportional share of the underlying reserves.
Since fees are added to liquidity pools, the invariant increases at the end of every trade. Within a single transaction, the invariant represents wusd / item at the end of the previous transaction.
There are many community-developed tools to determine returns. You can also read more in the docs about how to think about MP returns.
At the moment there are pairs with the protocol fees (also called Materia Fee). However, it is possible, by proposal, for a custom fee to be turned on for a single pair. Note that, even if the Materia fee is completely editable by the DFO, the total swap