1) 더위를 타시기도 하고 추위를 타시기도 한다
2) 더위를 타기도 하시고 추위를 타기도 하신다
3) 더위를 타기도 하고 추위를 타기도 하신다
I believe there is no hard and fast rule governing these things.
The common convention is to put the honorific form at the end as you said. So (2) appears the most correct to me, but (1) sounds natural too.
In (3) -고 connects two distinct clauses, so each clause should have its own honorific verb.
1) 전보를 기다리지 않으려고 해요.
2) 전보를 기다리려고 하지 않아요.
3) 전보를 안 기다리려고 해요.
There is some difference in meaning between them.
(1) and (3) are like "I try not to wait for the telegram" (I try to be more indifferent about it), while (2) is "I am not planning to wait for the telegram". So all three constructs are correct and may be used in some contexts.
But they are somewhat unnatural because negated -려고 하다 seems overly complex for the simple idea being expressed.
In (2), 기다리려고 하지 않다 sounds convoluted. We'd simply say 기다리지 않아요.
(1) and (3) expresses the attitude of trying to forget about it. For that, we are more likely to say 전보를 기다리지 않을 거예요 (I am not going to wait for it) or 전보를 기다리지 않기로 했어요 (I decided not to wait for [care about] it) .