1. I'm assuming your response to 2. indicates there is NO problem booting to your OS using the 120 GB drive even when the 240 GB drive is disconnected. That's right, yes?
2. That first partition D: on your boot drive - the partition you refer to as a "thing" you "accidentally made visible some time ago" - is probably the System Reserved partition with a different name ("idk"). I note it contains 59 MB of data - probably related to boot files.
3. I would think the sensible approach to take at this point is to delete all the partitions on your 240 GB secondary drive, i.e., the 450 MB one (probably a "Recovery" partition, and the F: partition which contains no data. You may not be able to delete those two partitions using Disk Management, and if so, you can probably use Diskpart to invoke the "clean" command so that the disk will become uninitialized. I assume you're familiar with Diskpart and its commands. If you're not, do a little Google research on using Diskpart.
4. After all the partitions on that 240 GB disk have been deleted, or the disk has been "cleaned" by Diskpart, you can create a single volume on the disk through initializing, partitioning, and formatting one or more partitions (as you choose).
5. Then you'll be able to use Disk Management to convert the disk to a Basic disk. There is no need for that disk to be a Dynamic disk. It will only cause you trouble.
6. Then you can use the disk as you see fit by creating one or more partitions and using the disk for storage, backups, or whatever.