Job Categories help you organize the jobs for easy management. They do not have any impact on the job execution.

or some job is switching the RECOVERY model to SIMPLE and back to FULL?

Is NTBackup scheduled to run on Wednesday? This can be a possibility.

Any blocking process?

It is not a good practice to truncate transaction logs. Please read through this[/url]

Is the "AutoClose" option enabled for that database?

None of the SQL Server related services show up in SQL Server Configuration Manager? Did you check in services.msc. If the SQL services do not show there as well, the...

Try running a Server Side trace with all the filters mentioned above. Running a profiler trace on a production instance might have negative impacts. An example here

The BACKUP command is failing because the Full Text Catalog 'db_catalog' is not online. Please navigate to FULL TEXT CATALOGS -> Storage and delete or enable "db_catalog". Try running the...

Just a guess. Is there another instance of SQL Server running on that server?

Add an output file to the Job Step (Edit Job Step --> Advanced). This will give more details on the job failure

From the error message it appears to be an issue with Database Mail. Please check if this discussion helps.

As others mentioned it is a truncated error message. Please include a log file to the job step...

I have used Idera Diagnostic Manager and it does a great job in monitoring the instances

I am no expert on compression. 7-zip[/url] does a great job when it comes to compression and it is open source too.