Your motherboard only fits a certain kind of apu/cpu that are all in the same amd family, FM2+, AM3+ etc, so will not accept anything of a different family like lga1155 or lga1150. So no, you'd need to change the motherboard to match the wanted cpu.
There are 2 types of graphics processors. The built-in on cpu (integrated gpu / igpu) which is the radeon HD, and non-integrated (add on cards) like the gtx1070. If your motherboard has the long pcie x16 slot directly under the cpu socket, you can use that with any modern gpu, so yes you could add the gtx1070 to the pc. The only issue there is the fact that the gtx1070 is an extremely powerful gpu, so much that it's going to be considerably more powerful than your current APU can use, so ends up being a huge waste of money. Kinda like owning a Ferrari when the only place you can drive it is up and down the driveway. A better match for the 6300 is the gtx1060.