Rumania was still allied with A/H at this point. Even after the outbreak of WW1 it waited two years before risking intervention. Why would it risk butting in when there is no general war to join, and they have no guarantee of finding any allies?
As for Serbia, it wasn't looking for a fight in 1914. Look at the way it accepted 90% of the Austrian ultimatum, despite having far more hope of Russian support than it would have in this situation, where it is launching an unprovoked attack for no reason except that it doesn't happen to like the Emperor.
That's true for 1914. But the OP's premise involves Franz Ferdinand taking the throne "some time in late 1910s", I'm guessing 1916/1917 (based on Franz Joseph's OTL lifespan). Many things will change by that time.
King Carol of Romania will die, and with his death A-H loses practically its only friend in the Romanian leadership. By 1914 Romania's alliance was already just polite neutrality - Carol himself declared that it's impossible to honor the alliance since public opinion in Romania is too strongly against A-H. After his death, the weak ties to A-H were and will be completely broken.
Serbia will mostly recover from the human and material losses of the Balkan Wars. It might not be confident enough yet to actively look for a fight, but if the Habsburg monarchy experiences such a huge breakdown of order as a civil war...ditto Romania. And they will likely not be alone.