What does it mean when the battery light comes on and the steering is hard when turning. There is power steering fluid in the vehicle and the battery is new.

This says it does have a fluid reservoir? Some electric power steering just has an electric pump as a opposed to a mechanical pump driven by the serpentine belt.

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The power steering warning light coming on in your car is bound to make you worried, especially as it tends to coincide with a total loss of power steering, making it much harder for you to steer your vehicle.
If you've ever driven a car with manual steering, you know how hard it can be. For vehicles with hydraulic power steering, the most common reason for the power steering warning light is that the fluid level is low. This is often caused by a leak in one of the hoses.
If you're driving along and you notice your power steering light come on which looks like a steering wheel with an exclamation mark next to it- you should park your car in a safe place as soon as you can, taking extra care as you'll be struggling a little with much heavier steering.
Open your bonnet and locate your steering wheel fluid reservoir. This may have an image of a steering wheel on the cap. If not, you may need to consult your owner's handbook to help you find where it is.

Do you mean the engine overheat warning? The power steering problem is most likely a defective steering rack, they always act up when hot due to internal seal leakage and fluid bypassing the seal.

Did you check to see if the serpentine belt is tight or missing? The battery light comes on to tell ou there is a problem with the charging system. It does not come on when the battery is bad. Since the alternator and the power steeringpu p are run Blythe same belt it would make sense to check the belt to make sure it is there and tight and capable of turning these accessories.

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Check the power steering fluid and make sure it isnt low. P/S means power steering.. meaning the you need to check the system. Usually this light come on when your low on power steering fluid.

Yes . A lose battery cable is like a weak battery. No B+ to power vehicle lots of things are not gonna work correctly.

check belt may be worn or loose -check power steering fluid level if low will cause binding and can cause belt to slip if alternator going bad can cause same or idler[tension] pulley going can cause slippage but most likely belt is worn and needs replacement

The battery light indicates either your alternator is gone or your battery has a fault. Start the vehicle and disconnect the negative battery terminal. If the vehicle continues to run replace the battery if the vehicle dies remove the alternator and replace it. The power steering pumps on fords are problematic at best. Once they get a whine in them they usually keep it. You need to repair the leak if you every hope to get rid of it. If you operated the vehicle for any length of time with the fluid low or empty you most likely will need to replace the power steering pump as you have blown the pump by running it dry.

Take the car in for a new serpentine belt and tensioner right away before you destroy the engine. The alternator, power steering pump and waterpump are not turning right now because the belt has come off. The battery will die soon because it is not charging, and the engine will overheat and perform it's own little rendition of the china syndrome. When the red warning lights in the dash come on, it generally means; park it unless you're being shot at.

• You have Electric Power Steering (EPS) not the traditional power steering pump. So there is no place to put power steering fluid in your vehicle.
  

• Hope this helps.