Understanding resistance in open and short circuits
The infinity means that the resistor is extremely high resistance so it can be ignored in comparison to the much smaller resistance(s) in parallel. 

For the same reason, anything shorted with an ideal short might as well not be there, so in the third case it's 12V/2\$\Omega\$ = 6A and eventually the 5A fuse should blow.

BTW, the first one isn't necessarily 3.4A despite their 'correct' answer. The internal resistance of the battery is specified only for i&lt;3A and for "short circuit" conditions. Since 3.4 > 3 but is not a short circuit, the current might be lower than 3.4A (or perhaps higher if you're paranoid).