SQL Server – Native Log Backup Running Every 5 Minutes

No. After you restored the database in your development environment it had become a different database. Re-attaching it back to production will replace the production database and all transaction that occurred after your initial detach will be lost. Doing what you describe usually require very complex solutions, involving setting up replication from production to staging and contiguously replicating transactions in production to the staging server. Needless to say, developing/testing such a complex solution is only worth it for a ... worthy goal. Shrinking your database is not such a worthy goal.

Handling situation of runaway data that was never designed for delete (which is 99% of all projects, since the need for efficient delete of data is never evident during development, when the tables are empty) is quite hard actually. Partitioning is the best solution, by far, but is a huge undertaking with serious impact on the application. Other than that, deleting old data in small batches is the next best thing, provided an appropriate supporting index is provisioned.

A partly online backup is certainly possible but switching to and back from archivelog mode needs downtime. As an alternative you could run in regular archivelog mode and trash the generated archived log files, until you run a backup.

For the backup to be recoverable it is important that it has ALL archived log files that were generated during the backup. End the backup with a log switch and also include those archives in the backup.

You must see this kind of backup as partially online. It does allow you to restore to the point in time where the backup completed, not to any other point in time. Very similar to regular offline backups, only, taken online. It saves downtime.

Why do you want this? This is a lot of effort just to safe maybe 10G of archive storage per day. It also introduces an extra error source and many dba's won't be able to work with this and expect to have all archives. My advice would be to keep it regular online backups, with regular archived log backups and keep things simple.