Don't expect the low ethereum gas prices to last. Ether Gas Station currently shows a cap of 6 gwei as being the safe low gas price for transfers. Etheremon is here to ruin the Ethereum network again.
Just last week, with the new Castle mode, Etheremon introduced battling. Now, those Etheremon sitting in their high castles on their mattresses full of experience are pretty tough to beat.
How do you beat an incumbent castle master? By training, of course. Etheremon have just recently introduced a gym mode, where you can take a single mon, and train it against three other mons. This also acts as another stream of revenue for the devs, as there's no reward other than XP given to the player involved.
As to cost? You're looking at about $6 Australian (closer to 4USD) for a training session. Perhaps soon, you'll be able to purchase yearly memberships for your etheremon.
Alternatively, if you want to ruin someone's day, you can still battle, for just the gas price, currently costing up to $4AUD.
The contract for trading, and lending mons to others is complete, but there's no word on the date when this functionality will be launched.