In Drupal 7 the db_result() function was removed. Instead you use fetchField() method after db_query(). Furthermore db_query() now takes an array of arguments, not string.
You should replace
$transaction_id = db_result(db_query("SELECT trid FROM {uc_dotpay_pl_transaction} WHERE order_id = %d", $arg1->order_id))
by
$transaction_id = db_query("SELECT trid FROM {uc_dotpay_pl_transaction} WHERE order_id = :order_id", array(':order_id' => $arg1->order_id))->fetchField()
and
db_query("DELETE FROM {uc_dotpay_pl_transaction} WHERE trid = %d", $arg1->transaction_id)
by
db_query("DELETE FROM {uc_dotpay_pl_transaction} WHERE trid = :transaction_id", array(':transaction_id' => $arg1->transaction_id))