I am in the middle of creating a quick video tutorial which I will post on youtube to show you how I would do this. I just need maybe another 10 minutes and I will post it as a reply to your message.
Here is a quick tutorial on how to remove 1 frame in Movie Edit Pro. I apologize for the flickering, I need to figure out why my system is producing that annoying glitch. By the way, just so you know, you are not talking to anyone from Magix here. This is a user forum so we are all users helping out other users. If this works for you please post a reply saying that it helped or it did not help.
I workarounded it zooming so much that I can see all individual frames on the timeline, and cut next to the desired one. But I really miss the dedicated buttons "Previous" and "Next" frame.
You can use the left and right arrow keys to move one frame at a time irrespective of the zoom level - however as you found you need to zoom in to delete the single frame - use Ctrl+Del and the gap wil automatically close.
For information you can do what you are doing quicker if you use the keyboard trim object shortcut keys - you will have to check the keyboard settings you are using - File, Settings, Keyboard - mine are as follows:-
T Split object at cursor
Z Delete from the beginning of the selected object to the cursor
U Delete the end of the object from the cursor
In your case the sequence would be (using my keyboard mapping):
Move cursor to start of frame to be deleted, press T
Press right arrow once, press Z.
Frame is now gone and gap closed - in two actions less then splitting the clip into three.
Also Ctrl + left or right arrow jumps along the timeline in 5 frame increments in either direction
It is worth learning these shortcuts they can save you a lot of time, clicking and zooming.