I have a 2015 Subaru Impreza sedan. I would like to increase the horsepower. I read that changing the exhaust system and adding a cold air intake would increase it and I also read it wouldn't?

I hear you, 'preza. The 2.0i is frustratingly slow trying to get this fairly hefty chariot rolling via its CVT. Nothing you can do about it. The 5sp manual is, somewhat surprisingly, much quicker, and gets only -2mpg penalty (on paper, anyway). What the Imp desperately needs is the room for the 2.5i from its big sister Legacy. With its CVT it's much quieter and faster, and still gets 32+ mpg hwy. Thus your best bet is to trade your Imp for for a Leg Prem (or Ltd) Sedan and enjoy some power, quietness, and space. It's a safer and cheaper (repairs on WRX!!) long term option than getting a "rex" or trying to squeeze your lemon more tightly. The 2.0i CVT exists for $5+ gallon fuel, and we're still a couple of years away from there.

Or I guess you can trade for the stick, knowing it's no fun in traffic, starting on a hill, and is challenging for the height-impaired driver.

Might now occur to me that you already have the stick. Then, indeed, the only choice is the Legacy 2.5i or a carefully-vetted WRX that you'll have to keep your fingers crossed throughout its shorter lifespan.