You might check the 'schedules' in the admin-console. The most important thing is, that no other backup-utility copies files from the data-directory... a FileMaker schedule copies the database-files safly to a backup-directory
its also possible to run a daily schedule in FileMaker and use another utility/backup-script to copy that FileMaker _backup_ once in a month
1) Schedules in the admin console do not allow any periodicity beyond weekly.
2) This has nothing to do with backup.
The server schedule can still be used to run your script. You just have to include code in the script that immediately exits without doing anything if it's not the first Monday of the month. Use a daily schedule for this.
Server schedule controlled scripts have some major limitations so not all scripts will run successfully from server schedules. This is particularly the case if they include an import or export records step. You should also check your script steps in the script editor for server compatibility by selecting that option in the compatibility drop down and checking for any steps that show in grey instead of black.
You can also continue to use the windows task scheduler. We use that for a script that imports records from one FileMaker file into another. (Can't do that from a server schedule for some reason.)
Set up a small "robot file" with no tables in it, just a small script that includes a perform script step to run the desired script in your hosted file. You will most likely need to define an account name and password for this file that matches an account in the hosted file that has sufficient access privileges for the script to run correctly. Use File Options to set this file to open itself with the needed account name and password and to run this script when the file is opened.