How can you be sure that your assumptions of the condition of the runway won't allow for a successful aborted takeoff before V1?
I can't, that's the whole point. I can't tell for sure if I'll stay on the runway or run off the end. I know for a fact that the odds are stacked against me.
Do you then brief it in your take off emergency briefing or is it something you decide if it happens, that you will continue before V1?
Yes, it will be in my briefing. V1 minus 5 and we go
How do you know how bad the fire is to the engine and that the engine is not severely damaged by the outburst of a fire and then producing no thrust?
To the first part, I don't know. The rest will show up on the engine instruments.
Where does your SOP allow you to disregard calculated FMC speeds and use one made up in your head?
My SOP allows me to deviate from any published procedures in the interest of safety. I have to justify it later. The fact is, I don't know if I can stop. I know I can continue (performance wise). If I GO and land safe, all is well. If I stop and stay on the runway, all is well. If I stop and run off the end, they still can't touch me since I've followed my SOP to the letter, but to me it's not the smartest or safest course of action (given the circumstances).