A:AnswerYes it is compatible. Google now let’s you group lights together. So if you name a group to LIFX lights and change color to purple they all should
A:AnswerIf the broken strip is the one connecting to the first strip in the starter kit I would think so. I would suggest not removing any of the backing on the extension and check it. If it all works, then secure it in place. I would think if that doesn’t work, you will need a new starter kit.