Time machine - 2 problems I can't solve

Time Machine problems... I have them. And I have given up after spending hours googling, reading, trying and getting nowhere. I really hope there is some experts out there who have the time and energy to help me out. So, here goes. Crossing my fingers!

Problem 1:

After putting a new hard drive in my old Macbook Pro, I did the first Time Machine backup a few days ago. Everything was fine until today, when I opened the Star Wars Display. I only have _one_ backup of my old hard drive along with about ten of my new hard drive. I have been using Time Machine for backing up to an external drive for over a year, so - where are all my old backups?

When I access the sparsebundle on my backup drive through Disk Utility, I get to Backups.backupdb > MyDriveName > about ten backup folders. The oldest being the same as I can see in the Star Wars Display.

I have checked the box in the Time Machine preferences which prompts Time Machine to tell me if older backups are being deleted. I have not gotten such a notification. So where are my old backups? Are they gone? If so, why? What did I do wrong? Why did Time Machine not warn me?

Problem 2:

I have an old backup on the same drive as mentioned above. It is not in the form of a sparsebundle but as a folder named Backups.backupdb. It has three years worth of backups. I have not been able to access them since I formatted my old hard drive a year ago and gave it a new name in the process. Since then, the backups have been placed in the above mentioned sparsebundle.

I am able to open the backup in the Star Wars Display by choosing this backup as an alternative drive holding down the option key when clicking on the Time Machine logo in the menu bar. But all directories are just empty shortcut folders - exactly as if I just open the folders in the backup folders in the Backups.backupdb folder. I hope that makes sense.

Is there any explanation for this? How can I access the folders, since they are not working in the Star Wars Display? Are the files gone?

Also, after I open the sparsebundle (from problem 1), it appears in Finder as a drive. Thus, I can access the sparsebundle as a regular folder. What will happen, if I move the Backups.backupdb folder to the sparsebundle? Can I try or will that just screw everyting up?

Bonus info:

In regards to space, my backup drive has 2 TB capacity. The sparsebundle has a size of 435 GB and the Backups.backupdb folder has a size of 53 GB. But when I check the info on the drive, only 58 GB of space is left. How does that make sense in any way?

English is not my native language, so I apologize for the ramble - it is hard enough to describe technical problems without writing in a foreign language.

If anybody chooses to answer me, know that I am not familiar with Terminal, but I can follow precise instructions 😉

Thank you!