Does anyone know how to fix the hatch trim properly? I recently bought the car used and I found it’s not installed correctly.

 

I think you are referring to Item *! (marked with a green ellipse) in the attached drawing. It is retained to a bracket with 5 plastic clips (center clip is marked with a red ellipse).
The mating part of the bracket appears to be bent (white ellipse), and someone appears to have attempted to fix a broken weld with epoxy (light blue ellipse).
Replacement clips are available at dealers and similar ones are sold by Amazon:

 

It is actually *2 in the diagram. The part in the blue eclipse is a metal hook that is supposed to hook into the plastic so I think I may have to remove *7 to properly get the side piece hooked in. I’ve added another photo for clarity.

 

The new photo is much more descriptive and clear. Item *2 is actually an antenna amplifier.
I agree with your conclusion that the 3-piece rear spoiler (Item *7) must be partially removed first.
If you look closely at the upper left corner, you should see (and feel) the seam between the left and center pieces. Unfortunately, to remove and re-fasten the left piece, the large top (center) piece must be removed first (though perhaps only partially)

In attached Image 1, is bracket "A" still fastened securely to the glass? I will assume "yes" for now.
The large center part of the spoiler is unfastened from inside with the hatch open. Refer to Images 2 and 3 for details.
Once that part is removed, the left piece can then be removed and re-fastened (bottom retainer first, as you surmised). Refer to Image 4.

The purpose of the tape is to prevent paint damage when using a nylon molding removal tool to release the clips.

 

I forgot to mentioned the center (upper) section of the interior hatch trim garnish is pried off with a nylon trim tool to expose some of the spoiler fasteners plus the 2 connectors.