$300 is tough
1) Oil change to synthetic oil (Amsoil, Mobil 1, Redline, etc.) It won't get you much hp, if any, but will reduce wear. $50. It WILL let you at least go the full oil change interval, 7500 miles, vs. 3k for regular oil, so it is a breakeven on cost but less of your time.
2) K&N cold air intake, $40 for just the drop in filter, $150-200 for the full cold air intake, if made for you IS.
3) Keep tires at FULL rated PSI. The 30-35 psi on the door jamb is for comfort and noise, for max speed AND mpg, fill to the rated pressure on the tire (40-55 psi), cost $0, mpg:. +1-2 mpg. If too noisy and stiff, back off until you like it.
There is no such thing as a $300 supercharger - those are scams - electric fans.
YES, you can downshift - that is WHY it is there. It does NOT hurt the tranny and it has protection to keep you from overrevving. I use the paddle shifters on my IS all the time - usually when I am preparing to pass and want the lower gear to start with instead of waiting on the downshift.