I'm having real trouble getting my head around these changes and I'm sure I'm not the only one.
To some extent I think it's harder that you knew how it used to work and are now having to re-adjust your existing habits, but yes. To some extent this happens whenever you have an established group of players and any major change is made. To another extent we need to do a better job of making this stuff clearer. I'm tempted to make anything you've outleveled simply shatter to clear up the confusion.
"I can use this equipment for 10 levels, and before then I need to find more gems from the higher level regions I'm then in, and craft something to replace my old stuff; be that a higher-tier replacement of what I already had, or a higher-tier version of something new." That's always been the core design, and we've just changed how the numbers look to make them scale more cleanly and clearly.
Is it correct to say that each tier is 5 civilisation levels and then you need to create improved higher gem spells to progress further?
Sure, and that's not new at all -- that was always the case.
So at my civ level of 17 I should have no problem taking on lower level reqions?
Generally speaking, sure. Also not new.
Also I can aim higher than my level and become stronger for a while?
Very much so -- also not new, although it's harder to do new (it was laughably too easy before). I recommend no more than about 4 levels above, in the main.