Make sure you don't have automatically report generation this can be the reason why the disk reach the threshold, yes you can send this report to email and I recommanded you to setup the external report center.
for the log it can be set automatic deleted base on how many days you want to keep the logs.

1. According to your first point, you are using the default setting where two options are selected only for Alarm not for auto deletion of logs, Disk Usage Alarm Options (i) 180 days and (ii) 85% Threshold it only gives you notification.  This is the reason your threshold is 87% which will not exceed to 90% because:
2.  According to your second point, you cannot set the threshold percentage because its automatically disable but you can set the days for auto deletion which will clear the disk after that days.

It can be only deleted automatically to the set days

Disk utilization is a measure of how much disk space is being used on a device. It is possible that the device is running out of disk space due to a variety of reasons, such as large files or applications consuming too much disk space. It is also possible that the disk is being used for logging or other system functions, which can cause the disk utilization to reach higher than normal levels. It is important to check the disk usage on the device to determine the cause of the warning.

IAM 12.0.13 User Manual. You can set mail warning information on the Alarm Options page. Auto Logs Deletion: Set disk usage threshold.