my specs is
cpu APU A8-3870K Quad-Core (socker fm1)
gpu r7 260x
ram 6 gb ddr3
psu Thermaltake litepower 450 watts
well will old processors like fm1 socket will run in new motherboard like amd fx motherboard
Answer about PSU:
Yes, It will work fine but overall it will work your PSU quite a bit. If you're like me and want the best life time out of your PC and not worry about power I would recommend a 750w PSU because It will cover you for pretty much any graphics card and other components.
For the motherboard question, please tell us what mobo you're planning on getting