My i20 Amaron battery was almost at 4 years, was noticing slow and longer cranks during cold starts, took it to battery guy and he tested it showed unstable battery but he said you can use. However there was couple months pro rata warranty left, he told me pricing if I used the prorata or just normal swap. Normal swap was cheaper as it’s their dealer pricing and not mrp.
with regards to the ac issues. When compressor oil turns black it means it burn the refrigerant and it’s acidic now.
in domestic and commercial air conditioning and refrigeration when this occurs, domestic it’s cheaper to change the ac and commercial change the compressor and add filters for suction and liquid line to prevent acid in system from destroying the new compressor after flushing the lines.
Now in automotive the compressor too pushes metal shavings around.
i had this happen in my Aveo, only changed the condenser and compressor, new compressor barely lasted a couple of months.
If you plan to sell it do the cheaper repair and notify next owner, else do a proper job of changing the expansion valve and condenser since the filter is in the condenser. And flush out the lines and evaporator using a good refrigerant line flush rated for r134a
And then make sure there is no moisture in lines by vacuuming the entire system after installation for atleast 30 minutes and only add the refrigerant by weight
local ac shops don’t follow this and never charge by weight nor add the required oil by weight and this damages the compressors.
Also with regards to an earlier post of the radiator,
You need to change the coolant at specified intervals listed on the coolant. And it’s optional to use a radiator flush.
For the airflow using a water hose from the front grills would be fine to wash of the dirt mostly