I can't definitively address all of what you say but the Bureau may do some extrapolation of total populations based on the surveys that are completed. Yes, there is a lot of data management done after all the field work is done. A lot of it is eliminating duplications. Based on surveys over years, not just the decennial full census, they have some idea what segments of the population get undercounted. How that is incorporated into the final report I don't know. The decennial census historically gets a very high level of cooperation from the public and a correspondingly high percentage of addresses get included in the census. And there are follow up operations to try to count those who for whatever reason didn't return a completed survey.
As for "temp" versus "real" that's not really meaningful for the census. The first two questions of the survey are:
"How many people were living or staying in this house, apartment, or mobile home on April 15, 2020?"
"Were there any additional people staying here on April 15, 2020, that you did not include in Question 1?"
It was up to the respondent to determine if they "live" at that address or not. If its a vacation home, temporary housing like a hotel, or anything like that they were supposed to indicate such and give the information for their "permanent" residence as of April 15. Remember people had several months to fill the survey out so they should have had a pretty good idea where they "lived" on April 15.
Ultimately it comes down to what the respondents told the Census Bureau. The Bureau collects the information given, it is NOT supposed to "correct" or "extrapolate from" what the individual tells us.
And yes by law participating in the decennial census is required and there is a potential $5,000 fine for not doing so. But all the field personnel were told that Bureau policy is to NOT bring that up or try to use it to coerce people into responding. If we were specifically asked by a respondent about that we were to confirm it and then drop it. We wanted people's voluntary cooperation. Possibly because coerced responses simply aren't reliable.
Does that clear up any of your questions?