On my most recent car before my current car, I put in a K&N air filter.
I believe I saw a minor improvement in horsepower, but it could also have been the placebo effect.
As to your questions:
You can save money with a K&N as long as the following are true:
- You clean/oil the filter at the recommended intervals
- You don't live in an excessively dirty environment (ala all dusty/dirt road driving)
- You use the K&N for at least three times the normal usage of a standard air filter.
For reference, I did a quick look up at autozone & the price comparison for the filter itself is $22 vs $67 (this is just in my area, but I believe the price will be proportionate anywhere in the US)
Yes this is true, I'm not sure how bad for the environment the oil for the filter is, but overall there is less 'stuff' created when using a K&N
Better for the engine:
This is the most debatable, K&N claims a much higher filtration efficiency & increased airflow compared to standard paper air filters. I believe that as long as you follow the instructions for whichever air filter you use, you will be fine.
As I alluded to earlier it's possible, but unless your car has a very inefficient air filter in it already, I doubt you will see much difference.