Welcome to TFP! Good to have you here
To maintain adequate sanitation in your pool, you need to use chlorine as well as your ionizer, so to answer the second question, an ionizer on its own is never working, including right after installation.
For outdoor pools, CYA is needed to protect the chlorine from sunlight, else it is depleted very quickly, so yes, you need CYA once you start adding adequate levels of chlorine to keep your pool safe. CYA also buffers the effect of chlorine making a CYA protected pool more gentle than some public pools, depending whether or not local public pool regulations are science-based.
Most if not all ionizers use copper, and some use silver as well. Copper in pool water is good at controlling algae but does not kill most pathogens quickly enough for adequate sanitation. When using chlorine, absence of algae is normally a good sign that sanitation is adequate, and conversely a warning system when it's not adequate. This warning system is lost in pools using only copper.
As time passes, copper will accumulate in your pool water, unless the water is drained and the pool refilled. Hence, adding copper to pool water adds a risk of staining the pool surface, and eventually hair and fingernails as the copper accumulates in the pool, hence why use of copper is never recommended as part of Trouble Free Pool Care (TFPC).
You can search a wide variety of threads here and also articles in pool school to learn more about effective and ineffective pool sanitation methods.
When you make the decision to adopt TFPC, there is heaps of help here for economic chlorination methods and low-cost water balancing generally. There's every chance there's someone here that has removed and knows how to remove your source of copper when the time comes.
EDIT: the gradual accumulation of copper in your pool water may be the reason you've sensed that copper-related problems get worse over time. That part is correct and variable because it depends on how much water replacement you experience. The lack of proper sanitation (if not using adequate chlorination as well as the ionizer) is an immediate effect.