What is 'naturally - in my analysis'?
'Well, you must have a civil authority you can trust. I thought perhaps that Mayor Orden might step down now and - well, if I were to take over his office, it and the military would work very nicely together.'
Lanser's eyes seemed to grow large and bright. He came close to Corell and he spoke sharply.'Have you mentioned this in your report?'
Corell said, 'well, yes, naturally - in my analysis'.

Does it mean:
1) based on the analysis of Corell, he would naturally become the Mayor after doing a big favor to Lanser
2) Corell mentioned his thought during analyzing in his report?Following sentences:
Lanser interrupted. 'Have you talked to any of the town people since we arrived - outside of the Mayor, that is ?'
"Well, no. You see, they are still a bit startled. They didn't expect it.' He chuckled. "No, sir, they certainly didn't expect it.'

What is 'it' in 'they didn't expect it'? Does it mean talking with Corell?

Question

What is 'naturally - in my analysis'?
'Well, you must have a civil authority you can trust. I thought perhaps that Mayor Orden might step down now and - well, if I were to take over his office, it and the military would work very nicely together.'
Lanser's eyes seemed to grow large and bright. He came close to Corell and he spoke sharply.'Have you mentioned this in your report?'
Corell said, 'well, yes, naturally - in my analysis'.

Does it mean:
1) based on the analysis of Corell, he would naturally become the Mayor after doing a big favor to Lanser
2) Corell mentioned his thought during analyzing in his report?Following sentences:
Lanser interrupted. 'Have you talked to any of the town people since we arrived - outside of the Mayor, that is ?'
"Well, no. You see, they are still a bit startled. They didn't expect it.' He chuckled. "No, sir, they certainly didn't expect it.'

What is 'it' in 'they didn't expect it'? Does it mean talking with Corell?

Answer

I agree with Olga naturally = of course

What is it?   I'm guessing based on the given information the townspeople didn't expect their arrival.

Answer

1) In the context above, "naturally"=yes/ of course
As for the meaning, your 2nd option makes more sense, as, according to Corell's reply, he mentioned his thoughts in the report.
2)"They didn't expect it"-(with no extended context given) I can only suppose that it may refer to the fact that the speakers arrivied in the city or some prior events which could have led to Mayor's resignation or the whole situation people were facing: war/economic turmoil/havoc /revolution.

Answer

I suspect you are right ans both (1) and (2) are correct, but I am not familar with teh book, sorry.

I suspect "it" is the military invasion. The people were not expecting to be invaded, perhaps. Again, not sure, without more context.