I am running a fixed effects model with schools being my level of interest. I want to understand which schools are getting the best marks after adjusting for student characteristics. I have 30 schools. I am doing the following:

Code:
xtset school_id
xtreg marks_end_year marks_beggining_year $student_characteristics i.discipline, fe base vce(robust)
Then to obtain the individual fixed effects I am doing the following:

Code:
predict fe_school, u
My understanding is that this will give me the deviation of each school's outcome from the regression constant term which is 1.238747 and corresponds to average outcome across units. Marks go from 0 to 3 in a continuous scale.

I have 3 quick questions:

1- for me to obtain the average outcome of each school I can just simple add 1.238747 to each individual fixed effect. Am I right?

2- I thought by using fixed effects we would always require to set a reference unit, so our fixed effects would be in comparison to that unit. And that random effects would give us the fixed effects around 0 so like around a central value. But if I run xtreg, fe and then get the fixed effects as per the above, I do get individual fixed effects that are deviations from the regression constant term, and not in reference to any particular unit. Can someone comment on this please?

3- how can I calculate 95% confidence intervals for those individual fixed effects u?