In response to your questions:
Why only fixed effects returns result in the HMP2 demo? Is it means that I need to set my disease effect as a fixed effect ?
Fixed effects are associations that you are primarily interested in, hence Maaslin2 reports them back (see next question for more explanation between fixed vs. random effect). In this case I’d set disease as a fixed effect.
What do you think is preferred in the example of BMI? categorical fixed or continuous random?
For BMI I would run both as a fixed variable, MaAsLin associated the bugs with what they are most associated with from the fixed effects in your model. Things we normally set as a random effect are technical confounding features such as sequencing batch, differences in kits… etc. or for longitudinal models the individual identifier is always set as a random effect. I would run separate models for the different BMI types if you want to both look at it as continuous and categorical.
We might have some batch effects, do you recommend to assign the different sequencing runs as random effect?
Yes, see above. That is completely justified as a random effect. If there is a wide range of sequence depths you can also use sequencing depth as a fixed/normal covariate.
My disease is binary (yes, no) is it any recommendation for associate with such case (maybe specific analysis method)? or influence any of the above?
Nope, that should be fine as a normal covariate in the MaAsLin model.
I hope this helps, please let us know if you still want some more details or any additional help we can give!