(i) This is to ensure that the connections do not contributed any extra, unknown, resistances in the circuit.

(ii) This is done to minimize the percentage error in the value of the unknown resistance.

Alternatively, This is done to have a better "balancing out" of the effects of any irregularity or non-uniformity in the metre bridge wire.

(iii) This can help in increasing the sensitivety of the merter bridge circuit.

Manganin / Constantan / Nichrome

This material has a low temperature (any one) of coefficient of resistance/high resistivity.

(a) The resistivity of a copper wire of very low. Also, the connections are thick, so that the area is quite large and hence the resistance of the wire is almost negligible.

(b) It is preffered to obtain the balance point in the middle of the meter bridge wire because it improves the sensitivity of the meter bridge. 

(c) Constant an is used for meter bridge wire because its temperature coefficient of resistance is almost negligible due to which the increase in temperature of the wire due to flow of current.