From what you say with the fault you will find the fan heater element is the fault here. Thats why its only getting warm in there on the fan setting as the warm will be the heat the fan will generate as it spins.
As when you use the fast heat up what this does is brings all the heater on at the same time so it will use the base heater and the full grill and the fan heater. So that will be why its working on fast heat as its using the other heaters to get hot.
What you need to do is emoty the oven and from there remove the back cover.
Behind there you will see the fan, Around the fan is the heater. Just check that and see if theres visable signs of it blowing on there. If so then you need to replace it.
If it looks fine then you need to remove the heater and test it with a multi meter to see if its faulty.
But from the sounds of this you will find the fan heater element is the fault here im afraid and will need to be replaced.
No worries, If you need anymore help just get back to me as you can reply back to me even after rating so that isnt a problem.
Looking at the picture the heater does need to be replaced. As to the wire you can just repair this as you will need a new amp tag and reconnect the wires to the new amp tag connector. You can get them from the likes of Maplins or even B&Q.
As to the heater im afraid we dont supply parts. But you can try this website as they sell all Samsung spares. Click here