Just want to know if a $26 chip will give me better gas milage and more power without causing damage to the rest of the engine?

I would save your money. Most people I know have been disappointed and felt they wasted their money.

If the big 3 automakers could plop one of those chips in their engines and increase gas mileage and performance, they wouldn't be going bankrupt right now.

I don't think any "chip" at any price will give you both better gas mileage and better performance.
There is always a trade-off between those two.
And, like Tx stated, most driver's won't notice the difference in most cases.