To answer for all your cpu related questions your laptop chipset supports and has been also sold with i7 sandy bridge cpu:s :
http://www.cpu-world.com/Sockets/Socket G2 (rPGA988B).html
All the i5 i7 - 3000 series cpu:s are ivy bridge and that is gen3 which is not supported dont bother with it. There is rare motherboards with that chipset which supports gen3 but yours dont, whatever bios mods you do that wont help.
Just pick i7-26xx model, atleast i7 2630QM and i7-2670qm works (later one is 4 core 8 thread) .
thing is these cpu:s raise your thermals through the roof. Workaround is to either use best non conductive thermal paste like thermal grizzly kryonaut and laptop cooling pad or modify the heatsink, add thermal pads to move heat from chips to laptop case. Looking more closely i7-27xx and newer sandy bridge cpu:s have different core stepping which might of been added in later bios firmware updates, or you might have to look for bios mods. To be safe i would get 4 core 8 thread i7-2670qm to save some time.
You can also upgrade ram to 2x4gb 1333MHz (PC3-10600) buy used to find cheap deal. (not needed unless you get egpu)
Laptop also supports sata3 speeds so SSD would be great idea and its never waste of money cause you can use it in new laptop /desktop pc aswell later on.
One last point is you gain literally nothing from getting i7 cpu unless you get eGPU setup from the wifi slot (mpcie) , asus motherbaords wont whitelist egpu:s so you should make this work, example here (forget that awful GPU casing he has going there) :
View: https://www.youtube.com/watch?v=-2qVZnGipUk
More reading on egpu here :
https://egpu.io/best-egpu-buyers-guide/#mPCIe-interface