Does premium gas hurt a motor rated for regular (87)? also does premium gas add horsepower?

No premium will not hurt an engine rated for regular.  Premium and regular have the same amount of energy in a gallon, the way you get more horsepower out of premium is the way the engine is able to use it.  With premium, the engine is able to advance the timing as premium is harder to ignite. Advancing the timing at higher rpm's gives you more power. I have a 2018 mustang that is rated for 460 HP with premium but I run regular in it, I lose some horsepower but do not want to spend 60 cents per gallon more for premium gas.  My engine has 4 knock-sensors in it so when pre-ignition happens the computer retards the timing.  Most modern engines have knock-sensors but if an engine doesn't and it is rated for premium and you run regular you run the risk of destroying the engine.

Depends on the Mustang. For the 2011+ Mustang GT's with the coyote, they will run fine on 87 octane, but only achieve the advertised HP and fuel economy on premium. 

For the Ecoboost Mustang, there's about 20-30 HP swing between 87 octane and 93 octane. 

For the V6 Mustang, there is no benefit to using premium. 

For the S197 Mustang GT, for 05-09 model years, there is no benefit. For the 2010 model year (last year for the 3 valve, and the only year the S197 Mustang GT got the previous Bullitt's (08-09)'s engine refinements (different tune and an improved air intake). Then there is benefit to using premium, but the car will run on 87 octane fine. 

For the New Edge Mustang GT, there is no real benefit to running premium

Using higher octane gasoline in a motor that doesn't require high octane gas is a waste of money. The octane number represents that more inhibitors are added to the gas to stop pre-ignition caused by heat and compression. Low octane gasoline burns better then high octane gas.

A modern car, like a new Prius, would require 87 octane, and higher octane would cause it to ping and ruin the engine (unlike old engines that would show no difference, but merely waste money).  Some engines are more powerful with higher octanes, and the Mustang engine could very well be one.   I suggest 87 octane.

You will waste your money on premium if your car calls for 87.

Those who answer that it will make zero difference are basing their opinion on obsolete technology . . . pre-computer  ignition & fuel systems led to detonation (knocking, pinging) on too low-octane with a higher compression engine.  Now computers allow engines with 10 or 11 to 1 compression ratios to run on 87 octane, because the computer will adjust timing and mixture to avoid those problems . . . but, of course, the engine isn't realizing its full potential.  It stands to reason that a higher-performance engine will also adjust when running on higher octane.

I had a Chrysler 300 and the Owners Manual actual stated the maximum horsepower developed on 87 octane, 89 and 92.  Yes, it ran fine on 87 but was noticeably more powerful on 92.

There's no point in using 92 octane in a Kia Soul or such . . . but there will be improvement in a V8 Mustang or Camaro.  You'll note that some hi-perf cars like a Jag require premium . . . . while a econobox with exactly the same compression ratio will call for only low octane.  Likewise, a miserable little Smart car with a tiny engine requires premium because they need to generate as much power as possible.

Other "experts" will disagree . . . . I go with my actual experience.  It certainly won't hurt your car to try a tankful or two and see if there's a difference.  You won't notice any difference puttering around town or driving at a steady 65 on the highway . . . . the difference would be most noticeable when driving in a mountainous area or when you really put your foot to the floor !

The answer is not usually, and no.

Premium gas, is actually "retarded" gas. And I don't mean that as an offensive statement, I mean it literally.

Higher octane gasoline means that Gas ignites and burns slower. Thus, it's retarded.

Your engine pulls gas into its cylinders (in a mist from the injectors) and ignites them at a specific timing, your spark plugs fire when each piston is open, so your (assuming) v6 has 6 cylinders that work in a varying firing pattern. The engine is designed to be used with 87 octane and that engine works under peak performance for that design. 

If you put in 91 or 93, you are slowing the burn and the motor is not timed right to that. You are actually reducing both performance (slightly) and gas mileage. 

Likewise if you use 87 in a car designed for 93 you are not allowing the gas to burn long enough and you are getting faster ignitions (reducing peak power). This is also what causes engine "ping"

However new cars are very often designed with a controller that will adjust the ignition speed if the other gas is used, but this is typically for 93 (premium) to run on 87, not for cars that take 87 to run on 93. Cars that take 87 should only use 87. It does not thing beneficial at all, and more then likely, actually does negligibly worse. 

So if that wasn't long winded enough... stop putting 93 in your 87 car, you are not doing anything besides wasting money. 

The improved performance is all in your mind.  But premium gas  won't hurt anything either....except your wallet

It won't hurt the engine. It will only hurt your pocketbook. The various octane blends are designed to prevent pre-ignition of the engine and nothing more. Different engines have different compression ratios and that is the basic need for the various octane blends. 

Putting in gas of a higher octane rating than needed will NOT hurt an engine.

However, it also does NOT help it in any way. It is simply a waste of a lot of money.