Q: How use Time Machine on new MacBooks?!!

Since it is not possible to use a USB HD and the MacBook charger at the same time on new MacBooks with USB-C

Not true. That's why they sell the adapter. http://store.apple.com/us/product/MJ1K2AM/A/usb-c-digital-av-multiport-adapter?f node=51

I'm having the same problem, and I don't think this is really a fix -- I shouldn't have to spend $ 80 more in order to backup my HD.  it should work "out of the box" as they say.  Is there any other solution?  any way to pause the backup in order to charge the macbook?

thanks!

No, but you should be able to complete a backup on a full charge.

You should have known that there was only one port before you bought it. If it had more than 1 port it wouldn't be its current dimensions. It was thinned down by design to where only one port would fit.