Past tense writing for history

When speaking of an action in the past, you use the past tense. This is a simple rule. But, when you are speaking of an action that involves an ongoing description of something that took place in the past, then you can mix the tenses as you have above. The example sentence you've given is just particularly complex, so let's break it down and see if we can understand what's going on.

If you look at your sentence, you're talking about the past action of suggesting something. In this case that one must approach ...

If we make the sentence simpler, we can see the following structure emerge:

This suggested that we approach the problem differently.

It would not then be necessary to switch to the past tense after the word suggested. It wouldn't really be logical to say:

This suggested that we approached the problem differently.

The only thing that actually took place in the past was the suggestion. What was suggested to the people in question was in their present. Hence we'd use the present tense. (Many languages would use an imperfect tense here, but English doesn't always have a conjugation for that.)

With regard to your second question, it is perfectly reasonable to use a singular case in cases where the consideration itself is singular. (i.e. There is only one atmosphere, state of affairs, or condition). I would probably use the singular for atmosphere and state of affairs as these concepts tend to be all encompassing. But pluralize conditions as there is usually more than one condition at play.

As an aside, I would likely split your sentence into two just for readability:

This suggested that one must approach the interpretation of a historical figure with consideration to the prevailing atmosphere, state of affairs, and conditions present with respect to that period in time. Only then would one be able to accurately evaluate a historical event or figure.