Some issues with kill_idle_transaction implementation at InnoDB level

Looking at following:

   if (trx->state == TRX_ACTIVE
       && trx->mysql_thd
       && innobase_thd_is_idle(trx->mysql_thd)) {
    ib_int64_t start_time = innobase_thd_get_start_time(trx->mysql_thd);
    ulong thd_id = innobase_thd_get_thread_id(trx->mysql_thd);

    if (trx->last_stmt_start != start_time) {
     trx->idle_start = now;
     trx->last_stmt_start = start_time;
    } else if (difftime(now, trx->idle_start)
        > srv_kill_idle_transaction) {
     /* kill the session */
     mutex_exit(&kernel_mutex);
     innobase_thd_kill(thd_id);
     goto rescan_idle;
    }
   }

a) It exits the kernel_mutex before killing the thread.

    i)Is it not possible that thread state can change (from sleep to
running) after mutex is exited?

    ii)If it is not possible to kill thread with kernel_mutex is held,
then it is not better to scan the trx list fully and then kill them at
once since thd_kill holds mutexes as well.

b) Is

    if (trx->last_stmt_start != start_time) {
     trx->idle_start = now;
     trx->last_stmt_start = start_time;

    required since thd->start_time (used by innobase_thd_get_start_time)
means the time the thread was in that state (in this case IDLE), so
doesn't thd->start_time > srv_... should state if it was idle that long?

c) Another issue (not sure if it can be fixed), is that this
runs every second in error thread, is it possible to not skip the
idle code for every few iterations (so as to run it every 60
seconds or configurable time) since otherwise the overhead of
this can be high.