1. Once triggered, transistor in avalanche breakdown is not controllable by base voltage. Pulse is either terminated by suitable designed output circuit or transistor will be destroyed.
2. Slow rising trigger can work under circumstances but expect reduced output pulse quality.
3. It's generally assumed that the voltage range for avalanche breakdown operation is between Vcb,max and Vce,max. Also that transistors with thin, low doped epitaxial layer are preferred.
I haven't yet seen avalanche pulsers with operation voltage < 50 V.