# How to interpret elastic net coefficients for multinomial regression?

I ran a elastic net regression path for a multinomial model using the glmnet package in R. My response variable has 3 levels (0, 1 and 2 for 3 different stages of a disease).

Here are the coefficient output from the elastic net

# Stage0
# (Intercept) -0.14301343
# Age          -0.16305154
# Q1       -0.04925107
# Q2       0.01030530
# Q5      0.11559569
# Q9      0.01927071

#Stage1
# (Intercept) -0.9571839
# Q5           0.4063393

#Stage2
# (Intercept)  1.10019732
# Q2      -0.04281563
# Q4      -0.07533350
# Q6      -0.01961934
# Q7      -0.15523562
# Q9      -0.03297465
# Q17     -0.06386999


My predictor variables are age, and Q1-Q18 for 18 items on a psychiatric questionnaire. I see that the elastic net shrunk certain coefficients to 0. My questions are

1) In the output above, the coefficients are separated by my response level (stage0, stage1, or stage2). What exactly does this mean? Is it that the coefficients under Stage0 are for the model when the multinomial model uses Stage0 as the reference level? How do I interpret these coefficients?

2) Can I take these remaining variables and fit a multinomial regression model? So instead of using all of my original 19 predictor variables, I can just focus on those that were selected by elastic net and do model building from there?