Yes I used to use one when ours were little. General advice is to get one with good big wheels. I couldn't afford one of those and ran with a more general 3 wheeler buggy with 12 inch wheels (fixed front wheel is essential!). It was perfectly fine running with it - I even used it a few times in my running club's monthly handicap race. Running up hills is a fair bit harder, along the flat not much different, and it is a help going down hill.
Generally not considered good to run with a real little 'un - wait until they are a good few months old and can support their head really well.
Remember when it gets colder they are just sitting still, and because of the excessive speed you will be travelling at, they can get very cold - wrap them up well, and put the raincover over as this keeps the wind off them. I would also say that although my kids in general loved it, that it is important to be prepared to be flexible and cut runs short if they are unhappy. For a similar reason if doing a longer run, use a route which brings you back near your house regularly rather than one big loop - running 5 miles back with a screaming child is not good for you or the child!
No problems with a bad back at all. I ran holding the handle one handed, and used the other arm to swing in the usual way, and then kept swapping over every few minutes. I would say it is important to get a buggy with a handle at the right height - my wife could never use that buggy as the handle was too high for her, and she found it especially difficult to push down to lift the front wheel to make it turn. See if a shop will let you test drive some different models. I'm afraid I'm not up to date with current models.
Great times - shame they are over, but I really don't fancy trying to run pushing my 14 year old now (or even the youest at 7!).