Range is definitely a limitation. Don't expect to transmit much over 3-4m away, and forget about from a different room in the house. Reconnection is okay, I find I need to be in range and then fire off a couple of shots in the camera to wake the eye-fi connection up.
Images transmit quickly when the connection is solid. I only ever transmit jpeg files wirelessly. A raw file would take a fair while to transmit.
I've not used an eye-fi to try to connect to an iPad. I only use mine with my Nikon DSLR, wi-fi router and Mac. It is possible to cut out the wi-fi router and link the card direct to the Mac, but I've found that to be very unreliable.
I get very frustrated with the software insisting on having an internet connection to be able to change certain settings. I don't understand why that is a requirement.
They are cheap and cheerful, you get what you pay for. They work fine, just don't let your expectations exceed what they are capable of. You could say that to pack a tiny wi-fi transmitter inside a SD card is a major feat in itself!
As someone else already mentioned, if you want something more reliable with greater range, go with a CamRanger.