I have a dataset with around 30,000 participants, clustered into 20,000 families which are further clustered into 7,000 households. I need to account for the family clustering which is nested in the household clustering when measuring my effect estimate. I am using Stata (version 15), my outcome is a binary variable, for this example my main exposure is a categorical variable and when I run my mixed effect logistic regression I am controlling for multiple other covariates as well.

the code is as follows:
Code:
melogit outcome exposure covariate1 covariate2 covariate3  ||household:||family:, vce(cluster household)
I have been confused when doing research on this topic, what is happening when there is another variable following the clustered variable like so,
melogit c_use age urban || district: age what is the 2nd age accounting for and is that something I should include?

Also, integration points, when should you change the amount of integration points you use and how do you use them, I know the default is 7 but I am not sure if I need to change them or how to interpret the output if I do.

Also, when using melogit are the point estimates accounted for clustering using fixed effects then the SE using robust at the household level? is it possible to change this or to use random effects, if so how do I do that?

The very last two parts what do the var(_cons) mean in these circumstances

Code:
Fitting fixed-effects model:

Iteration 0:   log likelihood = -6079.9391  
Iteration 1:   log likelihood = -5550.3319  
Iteration 2:   log likelihood = -5549.0637  
Iteration 3:   log likelihood =  -5549.063  
Iteration 4:   log likelihood =  -5549.063  

Refining starting values:

Grid node 0:   log likelihood = -5824.9555

Fitting full model:

Iteration 0:   log pseudolikelihood = -5824.9555  (not concave)
Iteration 1:   log pseudolikelihood = -5711.0415  (not concave)
Iteration 2:   log pseudolikelihood = -5555.8322  
Iteration 3:   log pseudolikelihood = -5522.1834  
Iteration 4:   log pseudolikelihood = -5521.3746  
Iteration 5:   log pseudolikelihood = -5521.3738  
Iteration 6:   log pseudolikelihood = -5521.3738  

Mixed-effects logistic regression               Number of obs     =     30,000

-------------------------------------------------------------
                |     No. of       Observations per Group
 Group Variable |     Groups    Minimum    Average    Maximum
----------------+--------------------------------------------
    household |      7,000          1        3.8         25
         family |    20,000         1        1.3          4
-------------------------------------------------------------

Integration method: mvaghermite                 Integration pts.  =          7

                                                Wald chi2(8)      =      59.79
Log pseudolikelihood = -5521.3738               Prob > chi2       =     0.0000
                              (Std. Err. adjusted for 7,000clusters in household)
------------------------------------------------------------------------------------
                   |               Robust
         outcome|      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
         exposure|
      2             |   .4139325    .074874     4.19   0.000     .1671822    .4606829
      3           |    .956007   .4214943     2.22   0.027     .1078934    1.760121
     4           |   .70234631   .1889264     3.74   0.000     .3370741    1.077652
                   |
         covariate1|  -.0023418   .0591824    -0.10   0.923    -.1216872    .1103036
        covariate2 |   .2345331   .0712209     3.69   0.000     .1233427    .4025234
         covariate3|   .013492   .0372542     0.40   0.686    -.0579577    .0880762
         covariate4|   .0163457   .0238631     0.70   0.484    -.0300612    .0634805
          covariate5|   .0343457   .0965659     0.36   0.722     -.154881    .2236504
             _cons |  -3.783458   .1728209   -21.92   0.000     -4.12689   -3.449445
-------------------+----------------------------------------------------------------
household        |
         var(_cons)|   .4873455   .1111736                      .3113988    .7623431
-------------------+----------------------------------------------------------------
household>family |
         var(_cons)|   .7645611   .2636417                      .3902342    1.5042231
------------------------------------------------------------------------------------