I do not think you need a Schottky bridge, any diodes will do.
I do not see how a regulator would be a benefit.
Some rough calcs, I'v oiled my abacus.
7 leds at 10mA = 70mA
Each will have a resistor but calculate the lot in parallel.
R = 13/0.07 = 186
Time constant = 10 sec = R*C
C =...