Discriminating and counting between filled columns and empty columns by sample row

I want to use Unix for the following. In a csv-file of 1,800 columns and 100 rows, looking like this

        Dog Cat Rabbit Horse Chicken
Sample1   0   2     10     0      30
Sample2  10   0      0     0       0
Sample3   0   40     0    20       0
Sample4   0   0     14     0      20
Sample5   7  13     25     0       0

The empty columns only have zeros, but I only want info on the filled columns.

First, I want to know how many columns are filled per sample; with the this amount being listed like:

Sample1 3
Sample2 1
Sample3 2
Sample4 2
Sample5 3

Second, I want to know which animals match each row:

Sample1 Cat,Rabbit,Chicken
Sample2 Dog
Sample3 Cat,Horse
Sample4 Rabbit,Chicken
Sample5 Dog,Cat,Rabbit