By 'trading if appropriate' are you referring here to maintaining the peg?

Yes, if the market HBD price is below $1, it will attempt to buy HBD or convert and if the price is above $1 it will attempt to sell HBD. If this can't be done, the tokens being held (whether HIVE or HBD) are returned.

As for interest, you seem to be confusing staked HIVE with HBD bearing interest (which would be a savings account). The stabilizer neither ever stakes HIVE nor ever places HBD into a savings account. Any staked HIVE which is received is powered down at the maximum possible rate, used for trading (peg maintenance) and returned.