a.) Its water repellant because its structure has no polar bonds or bonds capable of participating in hydrogen bonding. This makes the polymer hydrophobic and the bulk material water repellant.
b.) Alkalis (bases) generally donate electron pairs (Lewis Bases). Since the rubber structure contains electron rich pi bonds and saturated carbon centers, it is not likely that a base would react with it. Also, even if a base attacked one of the sp2 carbons, there is no way to stabilize the negative charge. Pi bonds are reactive towards strong acids, but much less so in the case of weak acids, which are poor H+ donors.
c.) Although the polyisoprene structure has pi bonds, they are not conjugated so there will be very little conduction along the carbon chain itself. Also, bulk rubber has a disordered structure (I am guessing) so there is probably little or no pi stacking so there will be no conduction between polymer chains. Hence, rubber is an electrical insulator.