I'll answer to your first question, even tough the whole request looks like a homework assignment...
Using direct current would cause the solution of which the conductivity has to be measured to start electrolysing thus not following Ohm's Law (IR=∆V) which allows us to find out the conductivity as the inverse of resistivity. On the other hand, if we use alternated current, the adsorbate on each electrode will electrolyse in the short time during which it's subject to a positive charge (for a 1000 Hz AC it's 10-3 s) and then return to its original state during the next moment, when the direction of the current is inverted. In this way there is no real electrolysis in the solution and it follows Ohm's Law (there are also methods using DC instead of AC to measure conductivity but they're much less precise than the other mentioned).