IPhone – use the Nexus 4 charger to charge an iPhone 4s

Most standard USB charges for 0.5A. But not all USB are standardized - there are some that go for up to 1.8A and even the MacBook Pro is said to raise up to 1.1A when relevant. iPhone's charger do little more than 1.1A and it's pretty decent. That's why iPhone charging on regular USB usually take double the time to fully charge. iPad's charger are roughly 10W and 5V which translates to 2A.

There's nothing wrong that can happen with the charger because USB devices are made to work with the same standard voltage (about 5V). The USB hosts are only outputting the maximum energy it can provide up to what the client can receive. A 10W energy source will only give up to 10W and just 1W if the plugged device can only take 1W.

I'm no electrical specialist but...

Having bigger power supply (measured in watts) or bigger current (measured in amperes) on itself can't break any system because what puts them in movement is the difference of potential measured by volts.

Think of a light bulb and picture all USB devices are prepared to receive about 5V (actually little more). If you get a 220V and put in on a 110V nothing wrong happens, but it will be very weak. Apple's chargers only go up to 5V, which is within the USB standard. So yeah, it's all good and safe.

Yes, it works great. The iPhone charges over USB like many other devices. The iPhone can accept more current than the USB specification, so you might have a slower charge than a charger that provides that extra wattage, but the iPhone circuitry is designed to take any normal USB charge and properly handle the charge which includes pausing it when the battery is full.