Yes, drivers have been published that will allow you to run on PC, hence, no need for any third-party software! [Source]
You can download the drivers for different build by using the links below or from Major Nelson's post I linked above as source.
Original dating back before 6 June 2014
No. The communication protocol the One controller uses is different from the communication protocol the 360 controller uses. This was needed to make several improvements such as reduced latency and more support for state messages for giving the console more control over the controller's state (it will put the controller in a low power state if you are not holding it).
But as you noted, all these improvements come at a cost. Until the time that someone comes up with a driver for the controller to be used on PC, there is nothing you can do. As X Padder relies on the protocol in use, it too won't be able to solve your issue. That being said, there supposedly is already a driver but because the protocol is likely protected by a patent, the driver would infringe on it. You can read some about it on this US Gamer article.