Replacing the entire rose is about as simple and straight forward a DIY job as anyone could possibly imagine. You only have a switch wire (red), neutral (black) and an earth wire (yellow/green) to worry about. Red needs to connect to the brown of the flex, black needs to connect to blue of the flex, yellow/green connects to a terminal on the rose marked E. Just make sure the power is isolated before touching anything. See if you can improve upon the single screw which holds the rose up though..
Not to secure the white flex TO anything - rather, just put it about the white bit, fairly tight, and that should prevent the flex slipping down through the hole in the cover.
It usually does - provided the tie is fairly tightly attached, the hole in the cover is not too big and the lamp/shade not too heavy.
If the hole in the cover is on the biggish side (relative to the cable size), you could try wrapping the tie around the cable two (or more) times - or using two ties.
However, as has been said, it would be very simple to replace the rose with one with actually had (intact) 'cable hooks' - which is obviously the proper' solution.
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