First, yes to the yellow things, that is the existing ptc fuse, and that is the existing mosfet gate pin.
The white mosfet and orange lines seems ok as long as gate drain and source pins are correctly used, for which the datasheet reading is a must. What i did said is that if you use the mosfet externally, have to remove the one on the board. That is because each gate has a parasitic capacitance which should be as low as possible, and if the old fet remains in place its gate capacitance would just add to the external gate and would double the parasitic capacitance - and that is not beneficial.
Then if you use the mosfet externally, you have to desolder the existing one, and then you could just use the existing one externally. From sources it should be STP55NF06L, which looks bit better than the sparkfun one. If you have that or not on your board, dunno, i guess depends on who manufactured your board, if its a clone its possible that things may slightly differ than the source. If you want a better and safer mosfet that wont give problems you can try IPS1011, but it is going to be expensive.
About the schematic link you gave, from www.electronics-tutorials.ws, that is sort of the case, and Rg and R2 are already on the ramps board. In that schematic the motor has an inductive clamp, you can also add a recirculating diode on the terminals of your heated bed. That diode would be any diode, cheapest 1N400x but you can desolder a diode from (almost) any recycle bin junk, and you orient it with the arrow in the opposite direction of the current flow, that is the arrow goes from the bed - to the bed + terminal. Physically best placement is on the bed terminals, on the principle of solving the problem at its source instead of dealing with it further away.
About the rest, you just have to feed power to ramps through the lower connector, that goes through smaller ptc fuse (5A) and supplies everything else (except the bed).
I think you got it. Good luck :)
The white mosfet and orange lines seems ok as long as gate drain and source pins are correctly used, for which the datasheet reading is a must. What i did said is that if you use the mosfet externally, have to remove the one on the board. That is because each gate has a parasitic capacitance which should be as low as possible, and if the old fet remains in place its gate capacitance would just add to the external gate and would double the parasitic capacitance - and that is not beneficial.
Then if you use the mosfet externally, you have to desolder the existing one, and then you could just use the existing one externally. From sources it should be STP55NF06L, which looks bit better than the sparkfun one. If you have that or not on your board, dunno, i guess depends on who manufactured your board, if its a clone its possible that things may slightly differ than the source. If you want a better and safer mosfet that wont give problems you can try IPS1011, but it is going to be expensive.
About the schematic link you gave, from www.electronics-tutorials.ws, that is sort of the case, and Rg and R2 are already on the ramps board. In that schematic the motor has an inductive clamp, you can also add a recirculating diode on the terminals of your heated bed. That diode would be any diode, cheapest 1N400x but you can desolder a diode from (almost) any recycle bin junk, and you orient it with the arrow in the opposite direction of the current flow, that is the arrow goes from the bed - to the bed + terminal. Physically best placement is on the bed terminals, on the principle of solving the problem at its source instead of dealing with it further away.
About the rest, you just have to feed power to ramps through the lower connector, that goes through smaller ptc fuse (5A) and supplies everything else (except the bed).
I think you got it. Good luck :)