Q1 No input current = 1A/.9 x Vout/Vin = 0.30525A this will increase as input voltage drops to 1A/.9 x 3.3/6 =0.6105A for the next bit use an average of 0.5A this gives a bit of margin as well.

Q2 Your cap C=I*t/dV

 dV is your brownout detect point say 11V-6V=5V

 t =5s (do you really need this long)

 I= 0.5A

 C=0.5F

This is in the supercap class go to farnell or one of the other suppliers and find the cap there.

Q3 You use a comparator one input is a divided down version of the cap voltage say 1/10 = 1.2V nominally. The other input is a stable reference (zener+resistor?) set at 1/10 your brownout detect voltage=1.1V. Make sure the comparator output is compatible with your mcu in. You may be able to find a 3.3 V supply voltage comparator.

Q1 No input current for a dc/dc convertor = 1A/.9 x Vout/Vin = 0.30525A this will increase as input voltage drops to 1A/.9 x 3.3/6 =0.6105A for the next bit use an average of 0.5A this gives a bit of margin as well.

Q2 Your cap C=I*t/dV

 dV is your brownout detect point say 11V-6V=5V

 t =5s (do you really need this long)

 I= 0.5A

 C=0.5F

This is in the supercap class go to farnell or one of the other suppliers and find the cap there.

Q3 You use a comparator one input is a divided down version of the cap voltage say 1/10 = 1.2V nominally. The other input is a stable reference (zener+resistor?) set at 1/10 your brownout detect voltage=1.1V. Make sure the comparator output is compatible with your mcu in. You may be able to find a 3.3 V supply voltage comparator.