I know it's been a long time to answer this question, but for those who may need:

For regular backups you can use a maintenance plan with the following schedule:

Take Full Backup for all User database at 5pm and another at 11pm

Between 11pm and 5pm you can create another maintenance (or add subplans) to take Log Backups.

It is not required to build a process to save information about what backups are being generated as SQL already saves

this info also you can see by checking the Job logs.

If they do want it, you can create a simple code within each job to add rows in a table you also create

to watch this.

If you still have any problem you can reach me at marcosfac@gmail.com