Answers to your questions:
1) Depending on the test you are trying to do, sometimes you'll be using the individual-level point estimates of part-worths (the average of 1000s of draws per respondent, leading to a single vector of utilities per respondent), sometimes you'll be using the individual-level part-worth draws (100s or 1000s of vectors of utilities per respondent), and sometimes you'll be using the sample-level part-worth draws (the "alpha" estimates, 100s or 1000s of vectors of utilities representing the average sample preferences). The point estimates are automatically output by the software without requesting anything special. If you want the individual-level draws (within the Lighthouse Studio HB estimation dialog), you'll be checking the "Save Random Draws" box on the Estimation Settings dialog. If you want the alpha draws, you'll go to the Advanced Output Options menu and click "Successive estimates of alpha (CSV).
The key thing is you need to decide if you'll be using Frequentist tests (in that case use the point estimates) or Bayesian tests (in that case you'll be using either the individual-level draws or the sample-level alpha draws...depending on the test you select that is described in Chapter 12 of the book you mention).
2) I usually do the tests by pasting the data into Excel...or directly opening the .CSV file or .XLS file in Excel.
3) For comparing different groups on part-worth utilities, decide if you want a Frequentist test or a Bayesian test.
Frequentist test: Make sure to use the point estimates (one set of utilities per respondent) and that you use the normalized utilities (zero-centered diffs) which are on a normalized and much bigger scale than the raw HB utilities. Then, take the normalized individual-level utilities plus the grouping variable into a program like SPSS, SAS, or R. Ask that software to compute an F-test, for significance between groups. Watch out for the fact that conducting so many independent F-tests can lead to false discovery of significant effects. Refer to section 12.3 of the book for remedies.
Bayesian test: You'll need to estimate the HB model with covariates in place, representing the groups you'll be comparing. You do that by clicking "Use Covariates" on the Advanced dialog in Lighthouse Studio HB estimation for CBC. Also, you'll need to request the alpha file output, as described above. Then, follow the instructions in the manual or follow the instructions in https://www.sawtoothsoftware.com/download/techpap/HBCovariates.pdf
to count for how many of the "used" draws (those draws after convergence is assumed) have (say) males thinking an attribute level has a higher score than the females. If (say) 99% of the draws after convergence show males having a higher utility than females on a given attribute level, then you are 99% confident that males have a higher utility (relative to the other levels within the same attribute) than the females.
4. With RFC and market simulations, you'll need to do a Frequentist t-test. Note that for each share of preference for the sample, we provide a standard error. Follow the same formula as expressed in section 12.2.d in Chapter 12 of "Becoming an Expert in Conjoint Analysis". That's the difference in share of preference between the two groups divided by the pooled standard errors of the shares of preference for the two groups.