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)
Less waste:
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.
More power:
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.